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Some Republicans are calling for Pence to replace Trump as their presidential nominee

He faced protests in Indiana over "religious freedom" and anti-abortion measures

Washington CNN  — 

Mike Pence has emerged as a popular alternative for top Republicans looking to replace Donald Trump as the party’s presidential nominee, but the Indiana governor’s own record with women could make it a short-lived courtship that doesn’t change the result in November.

Pence’s record on hot-button items from vowing to shut down the government over Planned Parenthood funding to graphic protests over his recent crackdown on abortion access, would make it difficult for Republicans to peel away suburban women voters from Hillary Clinton.

As talk of Pence replacing Trump bubbled up Saturday – sparked by top Republicans like Sen. Kelly Ayotte saying she was rejecting Trump and would write in Pence for president – Planned Parenthood quickly jumped on the attack.

“Trading Trump’s violent language for Pence’s devastating policy proposals is a horrifying substitution. Donald Trump and Mike Pence have been partners in the same agenda – and that’s what we have to reject,” Planned Parenthood President Cecile Richards said in a statement.

A campaign spokesman for Pence said Saturday he would “not engage in hypotheticals” over questions of Pence’s record.

In Congress, Pence was at the forefront of a conservative effort to block any federal funds from going to Planned Parenthood because the organization – which provides women with cancer screenings, counseling services and tests – also provides abortions.

In 2011, as he prepared to run for governor of Indiana, Pence told MSNBC that “of course” he’d shut the federal government down if congressional Democrats didn’t include the defunding of Planned Parenthood in negotiations to approve a spending bill and avert a shutdown.

“I think the American people have begun to learn that the largest abortion provider in the country is also the largest recipient of federal funding under Title X and they want to see that come to an end,” Pence said then.

When he campaigned for governor in 2012, Pence largely avoided talk of any hot-button social issues, including same-sex marriage and abortion. But as governor he has not shied away from those issues, notably stumbling in the polls after he signed a “religious freedom” bill last year.

That measure allowed businesses to decline services to same-sex couples if they cited religious objections. After days of intense national pressure – including a push by the state’s businesses to repeal the measure – Pence backtracked and approved a “fix” that said the law could not be used as a tool to discriminate.

Then, it was his cratering support among Republican women that helped pull Democrat John Gregg to a stunningly close rematch with Pence in the race for governor this year.

As he pushed for tougher abortion restrictions this year, Pence said that he was fighting to protect unborn life. He signed legislation this spring making Indiana only the second state in the nation to ban abortions in cases where women seek the abortion after learning the fetus has a disability.

“By enacting this legislation, we take an important step in protecting the unborn, while still providing an exception for the life of the mother. I sign this legislation with a prayer that God would continue to bless these precious children, mothers and families,” Pence said in a statement.

But that bill quickly drew a snarky campaign by women protesters called “Periods for Pence” – including a woman inviting Pence to her appointment with her gynecologist, an update from one woman about her cramps and other personal details about their periods.