Story highlights "I think we need to be very clear about what we can and cannot achieve," Paul Ryan said

"I think being an effective opposition party means being honest with people upfront about what it is we can and cannot achieve," he added

Washington (CNN) Paul Ryan doesn't believe Planned Parenthood should get one "red cent" from taxpayers -- but he cautioned Sunday against expectations that he'll be able to pull federal funding for the organization now that he's House speaker.

"I think we need to be very clear about what we can and cannot achieve and not set expectations that we know we can't reach given the constraints of the Constitution," Ryan told CNN's Dana Bash on "State of the Union."

Photos: Paul Ryan, rising GOP star Photos: Paul Ryan, rising GOP star Rep. Paul Ryan, R.-Wisconsin, was elected the 54th speaker of the U.S. House of Representatives on Thursday, October 29, after receiving the votes of 236 members. The vote was largely a formality after House Republicans nominated him for the position on Wednesday, October 28. Hide Caption 1 of 25 Photos: Paul Ryan, rising GOP star Ryan announced Monday, January 12, that he would not run for president in 2016, preferring instead to focus on policy work as chairman of the House Ways and Means Committee. Ryan, the GOP's 2012 vice presidential nominee, has long been seen as a top contender for the presidency. Hide Caption 2 of 25 Photos: Paul Ryan, rising GOP star Ryan, center, speaks with Rep. Devin Nunes, R-California, before a House Ways and Means Committee meeting on March 12, 2014. Hide Caption 3 of 25 Photos: Paul Ryan, rising GOP star Ryan and his wife, Janna, arrive at a state dinner at the White House in honor of French President Francois Hollande on February 11, 2014 . Hide Caption 4 of 25 Photos: Paul Ryan, rising GOP star Willie Robertson of the reality TV series "Duck Dynasty" poses for a picture with Ryan and his wife, Janna, before President Obama delivers his State of the Union address on January 28, 2014. Hide Caption 5 of 25 Photos: Paul Ryan, rising GOP star Ryan speaks at the Conservative Political Action Conference in National Harbor, Maryland, on March 15, 2013. Hide Caption 6 of 25 Photos: Paul Ryan, rising GOP star Ryan greets supporters during a presidential campaign rally with Mitt Romney at The Square at Union Centre in West Chester, Ohio, on November 2, 2012. Hide Caption 7 of 25 Photos: Paul Ryan, rising GOP star Rep. Paul Ryan of Wisconsin speaks during a campagin stop at the Iowa State Fair in Des Moines on August 13, 2012. It was the newly minted GOP vice presidential candidate's first solo stop since becoming Romney's running mate. Hide Caption 8 of 25 Photos: Paul Ryan, rising GOP star Ryan speaks after Romney announced him as his running mate in Norfolk, Virginia, on August 11, 2012. Hide Caption 9 of 25 Photos: Paul Ryan, rising GOP star Romney introduced Ryan as his running mate in front of the USS Wisconsin. The seven-term congressman provides a strong contrast to the Obama administration on fiscal policy. Hide Caption 10 of 25 Photos: Paul Ryan, rising GOP star Romney jokes with Ryan in April 2012 during a pancake brunch at Bluemound Gardens in Milwaukee. Hide Caption 11 of 25 Photos: Paul Ryan, rising GOP star Ryan looks on as Romney greets people June 18, 2012, during a campaign event in Janesville, Wisconsin. Hide Caption 12 of 25 Photos: Paul Ryan, rising GOP star Ryan speaks while campaigning for Romney at a textile factory in Janesville, Wisconsin, on June 18, 2012. Hide Caption 13 of 25 Photos: Paul Ryan, rising GOP star Ryan, left, and Romney greet each other on stage April 3, 2012, during the primary night gathering at The Grain Exchange in Milwaukee. Hide Caption 14 of 25 Photos: Paul Ryan, rising GOP star Ryan introduces Romney at a town hall meeting in Milwaukee, Wisconsin, on April 2, 2012. Hide Caption 15 of 25 Photos: Paul Ryan, rising GOP star Ryan is introduced before speaking about the federal budget at Georgetown University on April 26, 2012. Hide Caption 16 of 25 Photos: Paul Ryan, rising GOP star Ryan holds a news conference in December 2011 in Washington to introduce a package of 10 legislative reforms designed to revamp the budget process. Hide Caption 17 of 25 Photos: Paul Ryan, rising GOP star Ryan listens as Ben Bernanke, chairman of the U.S. Federal Reserve, speaks at the Committee for a Responsible Federal Budget annual conference in Washington on June 14, 2011. Hide Caption 18 of 25 Photos: Paul Ryan, rising GOP star Ryan looks over papers as he waits for other House Republicans to arrive for a news conference in the Capitol Visitors Center in 2010. Hide Caption 19 of 25 Photos: Paul Ryan, rising GOP star Ryan speaks to the media in 2009 about President Barack Obama's 2010 budget proposal. Hide Caption 20 of 25 Photos: Paul Ryan, rising GOP star Ryan, left, and Sen. Judd Gregg of New Hampshire speak to reporters about the 2010 federal budget. Hide Caption 21 of 25 Photos: Paul Ryan, rising GOP star Then-Budget Committee Chairman John M. Spratt Jr., left, and ranking member Ryan listen to Federal Reserve Chairman Ben Bernanke testify during the House Budget hearing on the economy on January 17, 2008. Hide Caption 22 of 25 Photos: Paul Ryan, rising GOP star Ryan follows President George W. Bush off of Air Force One at General Mitchell International Airport - Air Reserve Station in Milwaukee on July 11, 2006. Hide Caption 23 of 25 Photos: Paul Ryan, rising GOP star Ryan speaks at a Cato Institute briefing on Medicare reform in the Rayburn House Office Building in Washington on July 22, 2003. Hide Caption 24 of 25 Photos: Paul Ryan, rising GOP star Speaker of the House Denis Hastert, left, administers the oath of office to Ryan at the beginning of his first term as representative of Wisconsin on January 6, 1999. Hide Caption 25 of 25

The women's health organization has long drawn the ire of anti-abortion lawmakers, but efforts to pull federal funding for it increased after activists released undercover videos accusing Planned Parenthood of breaking federal laws by selling tissue and organs from aborted fetuses.

"I don't think Planned Parenthood should get a red cent from the taxpayer. I've always believed that, even before these disgusting videos came out," Ryan said. "But I believe we need to do our oversight. We're just beginning to start a committee to investigate Planned Parenthood. That's important. So the special committee on Planned Parenthood, I think, should be in the driver's seat overseeing this process."

Photos: The hand-off: How Speakers Ryan to O'Neill came to power Photos: The hand-off: How Speakers Ryan to O'Neill came to power The current Speaker of the U.S. House of Representatives is Paul Ryan, a Republican from Wisconsin. He gained his power from his predecessor, former Speaker John Boehner, after the Ohio Republican shocked the political world by deciding to vacate his position. Click through for other recent speakers: Hide Caption 1 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power Former Speaker John Boehner, a Republican from Ohio, gained his power from his predecessor, former Speaker Nancy Pelosi, when the GOP gained the majority of seats in the House in the 2010 midterm elections. Boehner announced his intention to leave the position in September 2015, and Paul Ryan succeeded him in October. Hide Caption 2 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power U.S. Rep. Nancy Pelosi was the first and only female speaker of the House. Her speakership lasted from January 4, 2007, to January 3, 2011. Pelosi, a Democrat, lost her seat to the Republican majority in the 2010 midterms. John Boehner took the gavel. Hide Caption 3 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power Dennis Hastert remains the longest serving Republican speaker in history, from January 6, 1999, to January 3, 2007. However, the GOP lost its majority in the House of Representatives, leaving Democrat Nancy Pelosi to become speaker. On Thursday, May 28, Hastert was accused in an indictment of lying to the FBI and evading currency reporting requirements as he sought to pay off a subject to "cover up past misconduct." On Thursday, October 28, Hastert pleaded guilty in the case. Hide Caption 4 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power Newt Gingrich broke the four-decade line of Democratic speakers by becoming speaker from 1995 to 1999 and was named Man of the Year by Time magazine for the accomplishment. He then fell from grace after a disappointing 1998 midterm election for the GOP, prompting him to step down from both the speakership and Congress. Gingrich's resignations came as a complete surprise to many, as the speaker had been fighting to keep his top job until the announcement. Hide Caption 5 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power Tom Foley, a Democrat who represented Washington state in the House for 30 years, took over the office of the speaker after the resignation of Jim Wright. Foley served as speaker from 1989 to January 1995 but was defeated in the 1994 election by George Nethercutt. Hide Caption 6 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power Jim Wright of Texas served two years as speaker, after Massachusetts Democrat Tip O'Neill retired. But he stepped down in 1989 after facing a House Ethics Committee investigation on improprieties with the sale of his book and fees from speaking engagements. He was the first speaker to resign in the face of a scandal. He died on May 6, 2015, at 92. Hide Caption 7 of 8 Photos: The hand-off: How Speakers Ryan to O'Neill came to power A Massachusetts Democrat who served as speaker from 1977 until retirement in 1987, Tip O'Neill was well-known for his deal-making as well as his collegiality with former President Ronald Reagan. Former Speaker Nancy Pelosi thought to commemorate the 34-year congressional career of O'Neill with an office building on the edge of Capitol Hill that bears his name. O'Neill was the longest continuously serving House speaker of any party in U.S. history. Hide Caption 8 of 8

Bash asked, "Will you defund Planned Parenthood?"

Read More