WASHINGTON — The Senate is expected to approve easily legislation that would keep the government open past a Wednesday deadline as its top Republican leaders stare down a right wing that’s angry that party leaders aren’t fighting harder to take away taxpayer funding from Planned Parenthood.

Majority Leader Mitch McConnell has moved to strip the measure of a provision that would cancel federal funding of Planned Parenthood, and top House leaders are going along, even as the controversy helped topple House Speaker John Boehner, who announced his resignation last week.

McConnell’s move has rankled conservatives such as Sen. Ted Cruz, R-Texas, a Republican presidential candidate, and tea partyers in the House who want the taxpayer money withheld from the women’s health care provider. Their demand follows the release of secret videos in which Planned Parenthood officials discussed the transfer of fetal tissue to researchers.

The White House signaled that Obama would sign the measure, called a continuing resolution, or CR, into law — if the House steps aside from the fight that tea party Republicans want over Planned Parenthood. McConnell, R-Ky., and Boehner, R-Ohio, don’t want the battle over Planned Parenthood to lead to a government shutdown.

Last week, Democrats led a filibuster of a Senate stopgap measure that would have “defunded” Planned Parenthood. That measure failed to win eight Republicans, leaving it short of a simple majority, much less the 60 votes required to overcome the filibuster.

Boehner’s shocking announcement on Friday that he’ll retire from Congress at the end of next month promises to ease passage of the measure through a shell-shocked House. Boehner had been struggling to overcome objections from lawmakers such as Rep. Mick Mulvaney, R-S.C., who strongly oppose passing a stopgap measure free of the Planned Parenthood language.

Boehner said Sunday the House would take up the Senate bill and also look at a select committee to investigate the video. The stopgap measure would require Democratic votes to pass.

“I expect my Democrat colleagues want to keep the government open as much as I do,” Boehner said on CBS’ “Face the Nation.”

Senate Democrats and most of their Republican colleagues are likely to help the measure over the 60-vote threshold Monday evening, setting up a final vote as early as Tuesday.

In the House, two key committees have released a draft of filibuster-proof budget legislation that would defund Planned Parenthood and keep a promise made during this spring’s budget debate to repeal key elements of Obama’s signature health care law. Panel votes are expected Tuesday and Wednesday.

The proposal would permit Republicans to deliver to Obama a measure to take away about $350 million in taxpayer funding Planned Parenthood now receives through the Medicaid program to provide health services to low-income women. Most of the money would be redirected to community health centers. It would also, after dozens of attempts, send a partial repeal of the Affordable Care Act to Obama’s desk for the first time, under fast-track rules for budget legislation known as reconciliation.

The measure would repeal requirements for most individuals to buy health insurance, as well as a mandate that employers of more than 50 people offer their workers coverage. New taxes on medical devices and generously subsidized “Cadillac” health insurance plans would be repealed, too. But popular provisions such as allowing parents to keep their children on their health insurance plans until they turn 26 and subsidies for lower income people to buy health insurance through federal and state markets would be retained.

Obama has threatened to veto the measure.