Rubio, a Roman Catholic, is opposed to abortion in all cases except to save the life of the mother. But if he were to win the nomination, Rubio's GOP rivals say, Democrats would win women voters by citing the Florida senator's opposition to abortion in the cases of rape or incest.
The attack highlights how the candidates vying for the GOP's establishment mantle are trying to convince moderate voters to reject the surging candidate starting Tuesday in the New Hampshire primary -- even though Rubio's position is in line with many social conservatives.
After Bush raised the issue Friday, his allies pushed on the matter just hours before Saturday's GOP debate.
In a CNN interview after a Bush rally in Bedford, Sen. Lindsey Graham, R-South Carolina, said Rubio's position is emblematic of Republicans Todd Akin of Missouri and Richard Mourdock of Indiana, who lost Senate races in 2012 because of gaffes over their hardline abortion positions.
"I'm pro-life. The most tragic thing in the world is for a woman to be raped, a child, a pregnancy caused by rape. I'm very pro-life, (but) I can't go there, I can't tell that woman you gotta carry that child," said Graham, a leading Bush surrogate. "I'm very pro-life, that's a sensitive issue, but I think in a general election that will be a hard sell."
Graham added: "He has no exceptions for rape or incest. Now, I respect the passion there but most Americans have a hard time going there."
On Friday, Bush made similar comments to CNN.
"Politically, it's a tough sell to tell a pro-life mother -- had her daughter been raped -- that she would just have to accept that as a sad fact," Bush told CNN's Jamie Gangel
. "This is not an easy decision, but Marco will have to explain that position."
Rubio spokesman Alex Conant referred an inquiry to comments the candidate made earlier this week after New Jersey Gov. Chris Christie also attacked the senator on the issue.
Rubio has said he would sign legislation to ban abortion even if such a measure included all three exceptions. But he reiterated that he is only personally in favor of an exception to save the life of the mother.
"I'm proudly pro-life, and I won't apologize for being pro-life," Rubio told reporters this week in Manchester. "I understand it's a difficult issue. When you find yourself in a crisis pregnancy, that's a very difficult situation. But I have to choose between the right of a person to do with their body with the right of an unborn child to live. And I choose to support the right of an unborn child to live."
Rubio added he'd win a general election argument over the topic with Hillary Clinton because, he said, she's an "extremist"
on the issue given her support for abortion even late in a pregnancy.