Republican lawmakers in both the House and Senate aren't ready to walk away from efforts to pass legislation repealing and replacing Obamacare, even if it means compromise among conservatives or working with Democrats.

"It needs to be handled," Senate Republican Conference Chairman John Thune, R-S.D., said Tuesday, just days after President Trump indicated the effort is over for now. "It's only a matter of time, I think, before it becomes clear something has to be done. Because Obamacare is in a death spiral and the insurance market is collapsing and we know that."

Senate Republicans remain eager to tackle health insurance reform after the House failed in its effort last week because they believe the current law continues to disintegrate, particularly in states where insurers have quit the health insurance marketplace and costs have spiraled upwards.

"It's imploding in my state," said Sen. John McCain, R-Ariz. "Something has to be done to protect the citizens and help them get health care they need and deserve."

But the Senate will continue to wait for the House to act, and Senate Majority Leader Mitch McConnell, R-Ky., made clear Tuesday he has no plans to take the lead.

"They went all out to try to pass a repeal and replacement," McConnell said of the failed House bill. "I'm sorry that didn't work, but our Democratic friends now have the law that they wrote in place and we'll see how that works out."

Early Tuesday, House Republicans met privately in the Capitol basement for the first time since last week's implosion of a repeal and replace plan that failed to attract enough GOP support. Rather than deciding to put the proposal aside and move on to tax reform, Republicans spent the meeting calling for another effort to produce a measure that can pass the House.

"After this morning, the resolve of our conference to repeal Obamacare and replace it has never been stronger," said House Majority Whip Steve Scalise, R-La.

White House Press Secretary Sean Spicer said administration officials have met with some Republicans about taking another shot at passing a bill.

"There is a discussion that began… of a lot of individuals on both sides of the aisle reaching out to both the president and key staff members to share ideas additional ways forward," Spicer said. "So there has been a discussion, and I believe there will be several more."

House Freedom Caucus Chairman Mark Meadows said his conservative faction is talking to moderate GOP lawmakers to find consensus on how to move forward. Freedom Caucus members made up the bulk of the opposition to the GOP's original plan, arguing it did nothing to lower the cost of health insurance.

"I think there is a real desire for everyone to try to find a way to lower premiums, and get to yes," Meadows told the Washington Examiner.

Trump called out the HFC on Twitter this week for opposing the health care bill, which the GOP was forced to pull from the floor on Friday.

"The Republican House Freedom Caucus was able to snatch defeat from the jaws of victory. After so many bad years they were ready for a win!" Trump tweeted.

Conservatives on Tuesday appeared more willing to accept that whatever legislation they can produce, it will not fully repeal Obamacare because of Senate rules that would prohibit many provisions from passing under special rules they will seek to avoid a Democratic filibuster. That means conservatives will have to compromise on a solution, some lawmakers said Tuesday.

"It is a tremendous conundrum," said Rep. Trent Franks, R-Ariz. "That is the essential cause of division in the House among Republicans. We can either readjust the objective, or overcome the impediment, and in my judgement we are going to have to do both."

Thune wouldn't rule out a possible deal with Democrats, pointing to Trump tweets suggesting health care reform could be bipartisan.

"The Democrats will make a deal with me on healthcare as soon as Obamacare folds — not long," Trump tweeted this week. "Do not worry, we are in very good shape!"

Thune said smaller bills to replace the measure "may be what they end up doing," but said the effort would be "entirely up to" the House."

The House passed legislation last week to repeal the health insurance anti-trust protection and it received nearly unanimous support.

"This is going to have to be dealt with eventually one way or the other, the question is not if, but when," Thune said. "The timing is now more in question but eventually something has to give and something will happen."