(CNN)The big battle over Zika could be coming to an abrupt end on Capitol Hill.
A growing number of House and Senate Republicans now expect Congress will soon pass a $1.1 billion funding package to combat the Zika virus without restrictions on Planned Parenthood, a move designed to overcome a filibuster by Senate Democrats and end the pre-election season with as little drama as possible.
Such a move would represent a win for the White House and congressional Democrats.
No final decisions have been made, particularly in the House where the dynamics are more complicated than the Senate. But negotiations have intensified over the last several days and final votes could occur as soon as next week in both chambers, according to senior GOP lawmakers and Republican officials.
The idea: To tie a must-pass bill to keep the government open beyond the September 30 fiscal year deadline with language to fund vaccines and research to combat the spread of the Zika virus. Senators are likely to reach such a deal, and many Republicans now expect the House to go along as well.
"I'd like to put it together," House Appropriations Chairman Hal Rogers, R-Kentucky, said of a Zika package and a bill to keep the government open.
In a private meeting convened Friday by House Speaker Paul Ryan, a vast majority of the 50 rank-and-file Republicans who spoke favored approving a short-term stop-gap bill until Dec. 9, several attendees said. A short-term bill is favored by defense hawks and appropriators, giving them a chance to reprioritize and potentially boost funding for certain programs in the lame-duck session -- rather than a long-term extension that would freeze lower levels of spending.
"I think the short term version is being strongly leaned to by the caucus," Rogers said.
But doing so would anger House conservatives who are calling for any funding bill to be pushed off to next year -- giving a new Congress and administration say in the spending decisions and avoiding action by a lame-duck Congress after this November's elections.
"I don't want a lame-duck," said Virginia Rep. Dave Brat, a member of the conservative House Freedom Caucus, who estimated between 50 and 100 other Republicans would vote against a short-term measure.
"I don't think it would be good," said Ohio Rep. Jim Jordan, chairman of the House Freedom Caucus. "We don't think big spending bills should be landing in lame-duck. You're going to let people no longer accountable to voters deal with a big issue like that."
But Congress is under enormous pressure to act on Zika funding in the wake of the outbreak -- after legislation has been stalled over a round of partisan bickering. Senate Democrats have blocked a $1.1 billion funding bill three times, citing language in the bill to ease pesticide spraying restrictions and to exclude Planned Parenthood from the list of providers to help combat the spread of the virus, which can be sexually transmitted.
Several Republicans exiting a morning meeting said it appeared increasingly likely that a clean bill -- without restrictions on Planned Parenthood -- would eventually be approved by both chambers of Congress.
"That's where we're headed," said one senior Republican in leadership.
But Ryan's office said discussions about a way forward were ongoing.
"No decisions have been made by House Republicans, and the discussions will continue," said AshLee Strong, a Ryan spokeswoman.
At the Friday meeting, Ryan laid out the various options for keeping the government open, while also expressing his preference to move smaller funding bills in an effort to avoid passing a major, omnibus spending bill at year's end. But he did not specify his preference for how to resolve the Zika stalemate.
The discussions come as congressional leaders meet with President Barack Obama at the White House Monday, in an effort to discuss the remaining business before Congress adjourns later this month to campaign ahead of November's elections. And Senate Republicans, in particular, are eager to return home given they are defending 24 seats this cycle and want to be as visible in their home states as possible.
Rep. David Jolly, a Florida Republican in a tough reelection race who brought a jar of mosquitoes carrying the Zika virus to the Capitol this week, said voters should "fire all of us" if Congress can't approve a clean funding bill this month.
"If we can't get Zika funding by the end of September then we are nothing but a bunch of idiots," Jolly said. "At the end of the day, if I had to place my bet it's going to be what we see every year - we're going to have 100 Republicans committed to the 'governing caucus' side with all the Democrats and accept the responsibility that we hold, which is to fund the government. We've seen this before -- it's deja vu all over again."
Pennsylvania GOP Rep. Charlie Dent said some members are still pushing to add controversial policy provisions that would make it difficult to pass. And in a swipe at some of these conservative members, he said, "We spend a lot of time around here taking advice from members who have no intention voting for bills."
Dent wants his leadership to move ahead with a short term bill that includes Zika money and possibly an appropriation bill that both sides can accept. But he worried that the House will lose any leverage with the Senate if the internal GOP split stalls action.
"If we have our usual circular firing squad discussions that go on ad naseum, then we'll get jammed," Dent said. "And I think everyone is very much aware that that's a likely outcome. I'd rather be doing the jamming than being jammed myself."