Washington (CNN) Donald Trump on Sunday repeatedly slammed his chief presidential rival Sen. Ted Cruz as a "total liar" as the Texas senator and his allies have claimed in the final stretch to the Iowa caucuses that Trump favors government-run, universal health care.

Cruz, meanwhile, pressed forward Sunday with the line of attack, proclaiming: "A vote for Donald Trump is a vote for Obamacare."

"Look, Ted Cruz is a total liar. I am so against Obamacare. I've been saying it for two years in my speeches, I'm going to repeal and replace Obamacare," Trump said on ABC's "This Week." "I don't even know where he gets this."

Trump is joined by his family as he is sworn in as President on January 20.

Trump is joined by his family as he is sworn in as President on January 20.

Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York.

Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York.

Trump apologizes in a video, posted to his Twitter account in October, for vulgar and sexually aggressive remarks he made a decade ago regarding women. "I said it, I was wrong and I apologize," Trump said, referring to lewd comments he made during a previously unaired taping of "Access Hollywood." Multiple Republican leaders rescinded their endorsements of Trump after the footage was released.

Trump faces Democratic nominee Hillary Clinton in the first presidential debate, which took place in Hempstead, New York, in September.

Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people."

Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people."

Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race.

Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race.

The Trump family poses for a photo in New York in April.

The Trump family poses for a photo in New York in April.

Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May.

Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May.

Trump appears on stage with singer Nick Jonas and television personality Giuliana Rancic during the 2013 Miss USA pageant.

Trump appears on stage with singer Nick Jonas and television personality Giuliana Rancic during the 2013 Miss USA pageant.

Trump speaks in Sarasota, Florida, after accepting the Statesman of the Year Award at the Sarasota GOP dinner in August 2012. It was shortly before the Republican National Convention in nearby Tampa.

Trump speaks in Sarasota, Florida, after accepting the Statesman of the Year Award at the Sarasota GOP dinner in August 2012. It was shortly before the Republican National Convention in nearby Tampa.

In 2012, Trump announces his endorsement of Republican presidential candidate Mitt Romney.

In 2012, Trump announces his endorsement of Republican presidential candidate Mitt Romney.

Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996.

Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996.

Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009.

Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009.

For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007.

For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007.

Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon.

Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon.

Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005.

Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005.

Trump attends a news conference in 2005 that announced the establishment of Trump University. From 2005 until it closed in 2010, Trump University had about 10,000 people sign up for a program that promised success in real estate. Three separate lawsuits -- two class-action suits filed in California and one filed by New York's attorney general -- argued that the program was mired in fraud and deception. Trump's camp rejected the suits' claims as "baseless." And Trump has charged that the New York case against him is politically motivated.

A 12-inch talking Trump doll is on display at a toy store in New York in September 2004.

A 12-inch talking Trump doll is on display at a toy store in New York in September 2004.

An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice."

An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice."

Trump putts a golf ball in his New York office in 1998.

Trump putts a golf ball in his New York office in 1998.

Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany.

Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany.

Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990.

Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990.

Trump signs his second book, "Trump: Surviving at the Top," in 1990. Trump has published at least 16 other books, including "The Art of the Deal" and "The America We Deserve."

Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989.

Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989.

Trump stands in the atrium of the Trump Tower.

Trump stands in the atrium of the Trump Tower.

Trump uses his personal helicopter to get around New York in 1987.

Trump uses his personal helicopter to get around New York in 1987.

Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric.

Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric.

Trump wears a hard hat at the Trump Tower construction site in New York in 1980.

Trump wears a hard hat at the Trump Tower construction site in New York in 1980.

Trump attends an event to mark the start of construction of the New York Convention Center in 1979.

Trump attends an event to mark the start of construction of the New York Convention Center in 1979.

Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City.

Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City.

Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school.

Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school.

Trump, center, stands at attention during his senior year at the New York Military Academy in 1964.

Trump, center, stands at attention during his senior year at the New York Military Academy in 1964.

Trump, left, in a family photo. He was the second-youngest of five children.

Trump, left, in a family photo. He was the second-youngest of five children.

Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer.

Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer.

President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House.

President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House.

The back-and-forth comes as Trump has pulled ahead of Cruz in the final days of campaigning in Iowa, where Cruz had been surging until Trump began lobbing attacks at Cruz, most notably raising the issue of Cruz's Canadian birthplace.

Cruz this week tied Trump's position on health care to those of Democratic presidential contender Hillary Clinton and President Barack Obama, accusing Trump of supporting "socialized medicine for every American."

Two super PACs -- the pro-Cruz Keep the Promise I and the anti-Trump Our Principles PAC -- have leveled similar attacks in ads posted days before Mondays' caucus.

"First there was HillaryCare ... then there was Obamacare ...we can't afford TrumpCare," alleges a Keep the Promise I TV ad running through the Iowa caucuses.

And Our Principles PAC posted a full-page ad Sunday in the Des Moines Register which claims in part that Trump "has called for universal, single-payer, government-run health insurance."

The accusations stem from a late September interview Trump gave to CBS's "60 Minutes" in which Trump suggested every American would have access to health care if he is elected president.

Photos: Texas Sen. Ted Cruz Photos: Texas Sen. Ted Cruz U.S. Sen. Ted Cruz has quickly made a name for himself. Since taking office in 2012, the Texas Republican has solidified his brand as a conservative firebrand willing to take on establishment members of the GOP. Hide Caption 1 of 19 Photos: Texas Sen. Ted Cruz Cruz speaks during the Republican National Convention in Tampa, Florida, in August 2012. Hide Caption 2 of 19 Photos: Texas Sen. Ted Cruz Vice President Joe Biden administers the Senate oath to Cruz during a mock swearing-in ceremony in January 2013. Cruz was accompanied by his wife, Heidi Nelson, and his two daughters, Caroline and Catherine. Hide Caption 3 of 19 Photos: Texas Sen. Ted Cruz During a news conference in March 2013, Cruz announces a plan to defund the Affordable Care Act, also known as Obamacare. Hide Caption 4 of 19 Photos: Texas Sen. Ted Cruz Cruz heads to the weekly Senate Republicans policy luncheon in Washington in March 2013. Hide Caption 5 of 19 Photos: Texas Sen. Ted Cruz Cruz speaks during the National Rifle Association's Annual Meeting and Exhibits in May 2013. Hide Caption 6 of 19 Photos: Texas Sen. Ted Cruz Cruz speaks during the "Exempt America from Obamacare" rally in Washington in September 2013. Hide Caption 7 of 19 Photos: Texas Sen. Ted Cruz Cruz emerges from the Senate chamber after spending more than 21 hours railing against Obamacare in September 2013. Hide Caption 8 of 19 Photos: Texas Sen. Ted Cruz Cruz speaks to reporters on Capitol Hill in October 2013. Hide Caption 9 of 19 Photos: Texas Sen. Ted Cruz From left, U.S. Sens. Lindsey Graham, John McCain and Cruz listen as President Barack Obama delivers his State of the Union address in January 2014. Hide Caption 10 of 19 Photos: Texas Sen. Ted Cruz Cruz leaves a briefing at the U.S. Capitol in June. The briefing was about the prisoner exchange that freed Army Sgt. Bowe Bergdahl from the Taliban. Hide Caption 11 of 19 Photos: Texas Sen. Ted Cruz From left, Cruz attends a Capitol Hill news conference with U.S. Reps. Marsha Blackburn, John Carter and Lamar Smith in September. Cruz discussed immigration reform at the news conference. Hide Caption 12 of 19 Photos: Texas Sen. Ted Cruz U.S. Sen. Pat Roberts, center, is joined by Cruz and former Sen. Tom Coburn at a rally in WIchita, Kansas, in October. Hide Caption 13 of 19 Photos: Texas Sen. Ted Cruz Cruz poses for a selfie following his February speech at the Conservative Political Action Conference in National Harbor, Maryland. Hide Caption 14 of 19 Photos: Texas Sen. Ted Cruz A woman piles up Cruz stickers during the Conservative Political Action Conference. Hide Caption 15 of 19 Photos: Texas Sen. Ted Cruz Cruz speaks Tuesday, March 10, during the Alfred K. Whitehead Legislative Conference and Presidential Forum in Washington. Prospective presidential candidates from both political parties participated in the forum. Hide Caption 16 of 19 Photos: Texas Sen. Ted Cruz "Late Night" host Seth Meyers interviews Cruz on Monday, March 16. Hide Caption 17 of 19 Photos: Texas Sen. Ted Cruz Cruz brings his daughters Caroline, left, and Catherine on stage during a walk-through Sunday, March 22, at Liberty University in Lynchburg, Virginia. Hide Caption 18 of 19 Photos: Texas Sen. Ted Cruz On that same stage, Cruz officially announces his campaign for the presidency on Monday, March 23. Hide Caption 19 of 19

"Everybody's got to be covered," Trump said in that interview, noting that his view might be "an un-Republican thing for me to say" and adding that "the government's gonna pay for it."

Asked if he was calling for universal health care, Trump said: "I am going to take care of everybody. I don't care if it costs me votes or not. Everybody's going to be taken care of much better than they're taken care of now."

Trump on Sunday strongly pushed back at Cruz and his allies' claims that he supports government-run, universal health care, noting that he says in nearly each campaign speech he gives that "Obamacare is a total disaster" and that he would "repeal and replace" Obama's signature health care law with something "terrific."

"I have a heart. I want people taken care of. If people have no money. We have to help people. But that doesn't mean single payer. It means we have to help people. If somebody has no money and they're lying in the middle of the street and they're dying, I'm going to take care of that person," Trump said on ABC's "This Week."

As he did in the "60 Minutes" interview, Trump said his plan would be to work with hospitals and doctors to set up a better system.

And then Trump took another dig at Cruz.

"I mean, maybe he's got no heart. And if this means I lose an election, that's fine, because, frankly, we have to take care of the people in our country. We can't let them die on the sidewalks of New York or the sidewalks of Iowa or anywhere else," Trump said.