As the Sept. 30 deadline to pass a government funding bill gets closer, GOP leadership is scrambling to avoid a possible shutdown over abortion politics.

At a party lunch Thursday, Senate Majority Leader Mitch McConnell (R-KY) laid out a plan to Republicans to prioritize a bill that would ban abortions after 20 weeks in the hopes of assuaging conservatives seeking to cut off federal funding to Planned Parenthood, CNN reported. The calls for defunding the reproductive health organization came after a series of sting videos that anti-abortion activists claim shows Planned Parenthood was profiting from the harvesting of aborted fetal tissue.

Any budget bill that defunded Planned Parenthood would likely be blocked by Democrats and vetoed by President Obama. GOP leadership has acknowledged that such a shutdown fight could have political consequences for the party, as Planned Parenthood’s popularity among Americans has continued despite the allegations.

“I think it’s nearly unanimous the view that a shutdown doesn’t defund Planned Parenthood, and it doesn’t help us maintain our majority so we can have some influence who the next members of the Supreme Court are and can elect a Republican president,” said Sen. John Cornyn (R-TX), the majority whip, according to CNN.

Likewise, the Senate GOP’s Number 3, Sen. John Thune (R-SD) also admitted the political costs of a shutdown when explaining to the plan to focus on the 20 week abortion ban, instead.

“I think there’s a good, strong co­ali­tion be­hind [the 20 week abortion bill] who want to see that bill de­bated, voted on, and so I think it’s cer­tainly something that’s con­sist­ent with ad­van­cing the pro-life move­ment,” Thune told the National Journal. “I think a lot of the pro-life move­ment also re­cog­nizes that a scen­ario that might end up in a gov­ern­ment shut­down would not be good for the cause.”

The 20 week bill passed in the House earlier this year and has already been introduced by Sen. Lindsey Graham (R-SC) in the Senate. A timeline to advance the bill has not been finalized yet, but aides suggested to CNN that a procedural vote to move it forward could be scheduled to the Pope’s visit later this month.

The question is whether conservatives rallying behind a shutdown fight over Planned Parenthood funding will get on board. Two of the Republican Senators pushing the defund effort, Sen. Ted Cruz (R-TX) and Sen. Rand Paul (R-KY) are running for president, in a campaign cycle geared toward bucking the establishment.

Also Thursday, the House Freedom Caucus — a group of 40 or so conservative members known for disrupting leadership’s plans — released a statement suggesting they weren’t looking to back down on the issue.

“Given the appalling revelations surrounding Planned Parenthood, we cannot in good moral conscience vote to send taxpayer money to this organization while still fulfilling our duty to represent our constituents,” the statement said, according to Roll Call. “We must therefore oppose any spending measure that contains funding for Planned Parenthood.”