Washington (CNN) Sen. Ted Cruz urged fellow Republicans Tuesday to quickly "honor the promises" the party made over the years to repeal Obamacare.

"2010, 2014, 2016, I believe were a mandate from the voters. We're tired of the premiums going up. We're tired of deductibles going up," Cruz said at a CNN town hall debate with Sen. Bernie Sanders over the future of Obamacare. "Should Congress move swiftly to repeal Obamacare? Absolutely."

Cruz and Sanders -- two senators with diametrically opposed views of government's role in health care -- faced off at the debate moderated by CNN's Jake Tapper and Dana Bash and featuring questions from an audience consisting of both defenders and critics of the Affordable Care Act.

Cruz's call on his party to "repeal every word of Obamacare" came as the GOP is grappling with how quickly to repeal the law. The party hasn't yet reached a consensus on an alternative to the law. President Donald Trump said Sunday that a replacement plan may not be rolled out until next year.

The town hall debate underscored the many challenges surrounding efforts to dismantle the Affordable Care Act -- a sweeping health care law that covers some 20 million Americans. The evening began with each lawmaker laying out starkly different views of the controversial law.

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"If you are one of 20 million Americans who finally has received health insurance, forget about it -- you're gone," Sanders warned about repealing Obamacare. "That means when you get sick, you ain't gonna be able to go to the doctor. And when you end up in the hospital, you'll be paying those bills for the rest of your life, or maybe you'll go bankrupt."

Cruz, a Texas Republican who made his name in national politics by fiercely opposing the health care law, said former President Barack Obama made a series of promises that were broken.

"If you like your doctor, you can keep your doctor," Cruz said. "Millions discovered that was not true."

Policy issues

Several policy questions are at the center of the ongoing battle about reforming Obamacare, including the popular provision to protect people with pre-existing conditions and the controversial mandate that nearly all Americans get coverage. Republican lawmakers are also wrestling with how to live up to their promises to make Obamacare more affordable and to reform Medicaid.

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The CNN debate highlighted how Republicans and Democrats fundamentally disagree on many of these issues.

One woman in the audience, Neosho Ponder, spoke about her fight against breast cancer and said she was undergoing radiation treatment. Ponder expressed fear that without Obamacare, she wouldn't be able to afford health insurance.

Cruz insisted that Republican lawmakers support prohibiting insurance companies from canceling coverage for someone just because they are sick. All GOP proposals that have been introduced to replace Obamacare with, Cruz said, "prohibit companies from jacking up the insurance rates because they got sick or injured."

Sanders was incredulous.

"Ted, I cannot believe what you just said. It's a direct contradiction of everything you ran for President on," he said. "What Ted has said is he wants to get rid of all federal mandates. Did you say that a hundred times?"

"I didn't say it once," Cruz said. "Virtually all of the Republican legislation that has been filed — that the Democrats have opposed — maintains a continuity of coverage."

The issue of pre-existing conditions came up again when Maria Shahid Rowe, a woman who is five-months pregnant, said she was worried she wouldn't be able to get health coverage without Obamacare.

Cruz responded that Democrats are mandating that people get "every coverage on earth -- and it sounds really good."

However, "you should get the policies that meet your needs," he said.

Sanders shot back that before Obamacare, Shahid Rowe's pregnancy would have been treated as a pre-existing condition. "What Ted is really telling you is they will not guarantee coverage for you."

Another woman in the audience, Melissa Borkowski, told Sanders she simply can't afford the health services she needs. Burkowski recently had an abnormal Pap smear, but said she couldn't get additional tests because she hasn't met her out-of-pocket deductible. Her fear: that she may now have undiagnosed cancer.

Sanders, who repeatedly stressed that Obamacare was far from perfect, said it is "totally absurd" that Borkowski has such an "outrageous deductible."

"If you were in Canada, you know what? You would get the health care that you need," he said. "The idea that we have policies like that, like the one you describe, is clearly an outrage."

Cruz lamented that coverage choices have gone down "dramatically" since Obamacare became law. The senator, whose Canadian birthplace became a political controversy during his 2016 presidential run, also added: "Bernie mentions Canada quite a bit. I know quite a bit about Canadian health care. I was born there. You know Bernie, that may be the best argument against your position. Look what it produced."

Sanders joked as he gestured at Cruz: "Look what the result is."

'Employer mandate'

Another key pillar of Obamacare that came up was the so-called "employer mandate" -- the law's requirement that small businesses employing 50 or more workers to provide healthcare for its employees.

LaRonda Hunter, who owns five hair salons in Texas, said she can't afford to provide coverage to her employees because of low profit margins and that the Obamacare rule is preventing her from growing her business.

Sanders responded with what he prefaced would be "an answer you will not be happy with."

"I'm sorry, I think that in America today, everybody should have health care. And if you have more than 50 people, you know what, I think I'm afraid to tell you, but I think you will have to provide health insurance," Sanders said.

Cruz shot back that Democrats have turned small businesses into a "bad actor."

"Millions of businesses are being told by Democrats: tough luck," Sanders said. "It's one of the most damaging things about Obamacare."

Photos: Moments from Ted Cruz's career Photos: Moments from Ted Cruz's career U.S. Sen. Ted Cruz, a Republican presidential candidate, speaks during a campaign rally at the Indiana State Fairgrounds on Monday, May 2. Hide Caption 1 of 24 Photos: Moments from Ted Cruz's career Cruz holds up the hand of Carly Fiorina at a campaign rally in Indianapolis on Wednesday, April 27. Cruz named Fiorina, a former presidential candidate, as his running mate. Hide Caption 2 of 24 Photos: Moments from Ted Cruz's career Cruz celebrates his Wisconsin primary win with his wife, Heidi, and Gov. Scott Walker in Milwaukee on Tuesday, April 5. Walker endorsed Cruz for the presidency. Hide Caption 3 of 24 Photos: Moments from Ted Cruz's career With his wife by his side, Cruz tours the Dane Manufacturing facility before speaking to workers in Dane, Wisconsin, on Thursday, March 24. Hide Caption 4 of 24 Photos: Moments from Ted Cruz's career Cruz speaks during the CNN Republican debate in Miami on Thursday, March 10. Hide Caption 5 of 24 Photos: Moments from Ted Cruz's career Cruz and his wife wave to the crowd at Liberty University after he announced his presidential candidacy in Lynchburg, Virginia, on March 23, 2015. Hide Caption 6 of 24 Photos: Moments from Ted Cruz's career Cruz speaks during the 2013 NRA Annual Meeting and Exhibits at the George R. Brown Convention Center on May 3, 2013, in Houston, Texas. Hide Caption 7 of 24 Photos: Moments from Ted Cruz's career Cruz poses with his wife, Heidi, and his daughters Caroline and Catherine. Hide Caption 8 of 24 Photos: Moments from Ted Cruz's career Cruz (left) fields questions from Bruce Rastetter at the Iowa Ag Summit on March 7, 2015, in Des Moines, Iowa. The event allows the invited speakers, many of whom are potential 2016 Republican presidential hopefuls, to outline their views on agricultural issue. Hide Caption 9 of 24 Photos: Moments from Ted Cruz's career Nobel Peace Laureate Elie Wiesel (left) listens as Cruz (right) speaks during a roundtable discussion on Capitol Hill March 2, 2015 in Washington, D.C. Wiesel, Cruz and Rabbi Scmuley Boteach (center) participated in a discussion entitled 'The Meaning of Never Again: Guarding Against a Nuclear Iran.' Hide Caption 10 of 24 Photos: Moments from Ted Cruz's career Governor Greg Abbott (center) speaks alongside Cruz (left), Attorney General Ken Paxton (right) at a joint press conference February 18, 2015, in Austin, Texas. Hide Caption 11 of 24 Photos: Moments from Ted Cruz's career Sen. Patrick Leahy (right) escorts Loretta Lynch back from a lunch break as Cruz (left) sits nearby during her confirmation hearing before the Senate Judiciary Committee January 28, 2015, on Capitol Hill. Hide Caption 12 of 24 Photos: Moments from Ted Cruz's career Cruz greets supporters at the South Carolina Tea Party Coalition convention on January 18, 2015, in Myrtle Beach, South Carolina. A variety of conservative presidential hopefuls spoke at the gathering on the second day of a three-day event. Hide Caption 13 of 24 Photos: Moments from Ted Cruz's career Cruz (left) and then-Texas Governor Rick Perry stand together during a press conference at the front gate of Fort Hood about Iraq war veteran, Ivan Lopez, who killed three and wounded 16 before taking his own life on April 4, 2014, in Fort Hood, Texas. Hide Caption 14 of 24 Photos: Moments from Ted Cruz's career (Left to right) Sen. Lindsey Graham, Sen. John McCain and Cruz listen as President Barack Obama delivers the State of the Union address on January 28, 2014, in Washington, D.C. Hide Caption 15 of 24 Photos: Moments from Ted Cruz's career Then-Senate Minority Leader Mitch McConnell (second right), poses with Republican senators-elect Jeff Flake (left), Deb Fischer (second left), and Cruz (right) at the U.S. Capitol on November 13, 2012, in Washington, D.C. Hide Caption 16 of 24 Photos: Moments from Ted Cruz's career Cruz speaks to reporters on September 25, 2013, after ending his talk-a-thon on the floor of the US Senate in Washington, D.C. Hide Caption 17 of 24 Photos: Moments from Ted Cruz's career Cruz speaks as then-Rep. Michele Bachmann (left), Sen. Mike Lee (second right) and Sen. Rand Paul (right) listen during a news conference May 16, 2013, on Capitol Hill. Hide Caption 18 of 24 Photos: Moments from Ted Cruz's career Cruz listens to testimony during a Senate Judiciary Committee hearing on April 22, 2013, in Washington, D.C. Hide Caption 19 of 24 Photos: Moments from Ted Cruz's career Cruz holds a news conference to announce the plan to defund Obamacare on March 13, 2013. Hide Caption 20 of 24 Photos: Moments from Ted Cruz's career Cruz speaks at the CPAC on March 6, 2014, in National Harbor, Maryland. Hide Caption 21 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks at the 'Patriots for Romney-Ryan Reception' on August 29, 2012, in Tampa, Florida. Hide Caption 22 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks during the Republican National Convention at the Tampa Bay Times Forum on August 28, 2012. Hide Caption 23 of 24 Photos: Moments from Ted Cruz's career Then-Senate Republican Candidate and Texas Solicitor General Cruz speaks during the Republican National Convention in 2012. Hide Caption 24 of 24

One more area where the parties diverge is Medicaid. Democrats championed expanding coverage for low-income Americans by expanding Medicaid to more adults. Republicans, on the other hand, want to curtail federal responsibility for the program by capping funding.

At Tuesday night's debate, Carol Hardaway shared that she has multiple sclerosis, which created challenges in her walking, speech and vision. When the Affordable Care Act passed, Hardaway said, she moved from Texas -- a state that has not expanded Medicaid -- to Maryland, which has, and was able to receive treatments right away.

Hardaway posed a question to Cruz that Republicans are struggling to answer: Can he guarantee that people like her would continue to be protected?

Cruz referred to Medicaid as a "profoundly troubled program" akin to "rationed care."

"We should have a system that allows as many people as possible to be on the private health insurance of your choice rather than Medicaid," Cruz said, noting that wait times under the program has gone up.

But when Tapper asked Hardaway whether Cruz had answered her question, she indicated that he had not.

Drastically different approaches

Cruz and Sanders both ran unsuccessfully for president in 2016 and have their own ideas on reforming the health care system and making coverage more affordable for everyone. Their approaches, however, are drastically different.

Sanders is a proponent of a " single-payer " federal health care system, or as he refers to it: "Medicare for All." During the presidential campaign, the Vermont senator outlined a government-run program that would offer Americans comprehensive care covering everything from doctors' visits to hospital stays, to vision, dental and mental health services.

He is a proponent of hiking taxes on the wealthy to pay for his proposed system.

Cruz, meanwhile, has railed against Obamacare for years and has vowed to fully repeal "every word" of the law. The Texas firebrand made his name in national politics in 2013 when he gave a more than 20-hour marathon speech to oppose funding for the Affordable Care Act.

Taking aim at pharmaceutical industry

Despite their contrasting views on health care, there was a rare moment of agreement for the two senators: the pharmaceutical industry. Sanders asked Cruz to partner with him in taking on drug companies -- "the greediest of many greedy corporate interests in Washington" -- by supporting legislation to have Medicare negotiate prices with the industry.

"I would love for us to work together in going after big Pharma," Cruz said, though he stressed that it is the U.S. Food and Drug Administration that is enforcing an important ban.

Congressional Republicans are paving the way to repeal significant portions of Obamacare. Senior lawmakers are currently crafting an Obamacare repeal bill that requires just a simple majority of senators for approval.

But the discussions over creating an alternative to the controversial law has exposed tensions within the GOP. Many Republican lawmakers have grown increasingly wary of the political consequences of a quick and sweeping repeal of Obamacare, and some have more openly begun to discuss "repairing" the law and keeping aspects of it that are popular.

That note of caution clashes with impatience among some conservative members of the GOP conference, who fear that anything short of a swift repeal of Obamacare will be unacceptable to their constituents.

Trump, who campaigned on repealing and replacing Obamacare, said over the weekend that rolling out a new healthcare system will likely be a drawn-out process

"I would like to say by the end of the year at least the rudiments, but we should have something within the year and the following year," Trump said.