Marco Rubio

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Sen. Marco Rubio, R-Fla. passes at left as Sen. Jeff Sessions, R-Ala., right, talks with reporters on Capitol Hill in Washington, Friday, Oct. 11, 2013, as Republican returned to the Capitol after a two-hour meeting at the White House with President Barack Obama, trying to come up with a bipartisan solution to the budget stalemate. (AP Photo/J. Scott Applewhite)

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Sen. Marco Rubio R-Fla. speaks during the Values Voter Summit, held by the Family Research Council Action, Friday, Oct. 11, 2013, in Washington. ( AP Photo/Jose Luis Magana)

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Sen. Marco Rubio, Florida Republican, gestures as he speaks at the Values Voter Summit, sponsored by the Family Research Council Action, on Friday, Oct. 11, 2013, in Washington. (AP Photo/Jose Luis Magana)

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Sen. Marco Rubio has pledged not to vote for any spending bill that would fund the Affordable Care Act, saying "there are some issues that are so fundamental that we have to be willing to go all the way." (Associated Press)

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Sen. Marco Rubio is now taking stands on issues that could win back some friends among conservatives who criticized his immigration reform effort. (Associated Press)

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** FILE ** Sen. Marco Rubio, once a darling of the tea party movement, has dismayed many of the people who helped put him in office with his immigration reform bill. (Associated Press)

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** FILE ** Sen. Marco Rubio, R-Fla. speaks at the Faith and Freedom Coalition Road to Majority Conference in Washington, Thursday, June 13, 2013. (AP Photo/Charles Dharapak)

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Susan B. Anthony List and other pro-life groups have been lobbying Sen. Marco Rubio, Florida Republican, for weeks to lead the charge in the Senate on legislation would ban abortions 20 weeks into pregnancy, with exceptions for risks to the mother's life and rape or incest, though such a bill is unlikely to be taken up in the chamber. (Associated Press)