WASHINGTON — (CNN) Senate Majority Leader Mitch McConnell is moving to separate abortion politics from a spending fight that threatens to shut down the government at month’s end.

His next move: Advancing a separate bill aimed at preventing abortions after 20 weeks into a pregnancy, according to senators briefed on the plan.

McConnell told Republican senators at a party lunch Thursday that he planned to begin the process of considering the bill next week, which would set up a procedural vote to coincide with Pope Francis’ visit to Washington later this month. Senators said it’s possible more anti-abortion bills could be considered, even though they stand virtually no chance of becoming law.

The move comes as McConnell and House Speaker John Boehner are beginning to take a series of steps to avoid a possible shutdown at month’s end. Conservatives are demanding that the must-pass spending bill should prohibit federal funding from flowing to Planned Parenthood in light of controversial, heavily edited videos secretly taped this summer where officials discussed the sale of aborted fetal parts. But McConnell and Boehner, recognizing that Senate Democrats would block any effort to defund Planned Parenthood and President Barack Obama would certainly veto it, are trying to lay out a complicated set of steps to extricate abortion politics from the spending fight.

As part of that effort, Boehner and McConnell are highlighting the series of investigations congressional committees have launched to explore Planned Parenthood’s actions and funding. They are discussing moving the issue to a separate process — known as budget reconciliation — to take on the organization without risking the closure of the government. They are privately making the case to their members that any shutdown would hurt the anti-abortion community’s cause.

And now, McConnell is preparing to move separate bills on abortion, giving his party the opportunity to show their opposition to abortion without threatening a shutdown.

“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-Texas, the majority whip. “Sen. McConnell has already talked about some pro-life legislation he will be filing cloture on at the end of next week. And I think we’ve been working with a number of folks in the pro-life community asking them the question, how can we advance the pro-life agenda, not how can we set it back by associating it with a disastrous government shutdown narrative.”

Whether this tactic will pass muster with House and Senate conservatives, however, is another question. GOP Sens. Ted Cruz of Texas and Rand Paul of Kentucky, two presidential candidates, are ratcheting up their public demands that Planned Parenthood be defunded — joining the conservative House Freedom Caucus that is pushing the strategy as well.

“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 caucus said in a statement. “We must therefore oppose any spending measure that contains funding for Planned Parenthood.”

Cruz missed the Thursday strategy session over lunch in the Senate’s Mansfield Room, senators said.

But on Wednesday, Cruz lashed the strategy of “meaningless show votes,” saying, “Washington is very good at games.”

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