(Jenny Starrs/The Washington Post)

Sen. Ted Cruz, a defiant loner whose feuds with Republican Party leaders have made him a conservative favorite, suddenly felt an itch to collaborate.

It was late March, just after the dramatic collapse of House Republicans’ initial attempt to pass a sweeping overhaul of the nation’s health-care system. Cruz (R-Tex.) sent notice to party colleagues that he wanted to convene a working group to keep alive the GOP’s pledge to undo the law known as Obamacare.

Now, in the days since the House reversed itself and approved a health-care bill, that group, which presently numbers 13, is at the center of a fragile connection between hard-liners and leadership that may be the Senate’s best chance to pass its own version. The strategy, according to interviews with two dozen Republican senators and aides, is to bring together lawmakers with starkly different views, let them talk — and keep them talking until consensus is reached, in a process that could drag on for months.

There’s one big problem: Many of the key Republican senators who could stand in the way of a successful health-care vote are not in the group. And some of them are forming their own coalitions, suggesting that the path to 50 votes in a chamber with only 52 Republicans remains deeply challenging.

According to several Republicans close to the discussions, the three biggest issues yet to be reconciled are the scope of coverage for people with a preexisting injury or illness, health-care tax credits and Medicaid. Many differences remain among members of the working group itself.

Sen. Ted Cruz (R-Tex.) on Capitol Hill this week. (Pablo Martinez Monsivais/AP)

Sen. Rob Portman (R-Ohio) and Cory Gardner (R-Colo.), who hail from states that expanded Medicaid under the Affordable Care Act, have repeatedly expressed concerns about being able to provide adequate protections for people who have received coverage through the entitlement program or may be eligible to receive it in the future.

“I’m sure people will be talking about it,” Gardner said when asked about the idea of lengthening the timeline in the House bill for rolling back the expansion of Medicaid.

Others, including Cruz and Sen. Mike Lee (R-Utah), have signaled that they want an uncompromising assault on Obamacare that goes further in shredding regulations than many Senate Republicans are willing to venture.

Sen. John Thune (R-S.D.), another member of the group, has been working on a provision to rework the tax credits in the House bill to provide more assistance to elderly and lower-income Americans. The House included tax credits in its bill as a substitute for federal insurance subsidies in Obamacare.

There are other differences among Republicans. For starters, the group is made up of 12 white men plus Cruz, whose father is from Cuba, and has generated critical headlines and television coverage for not including any of the five female Republican senators.

“Those are choices that were made,” said Sen. Shelley Moore Capito (R-W.Va.), who objects to the House bill’s impact on her rural working-class state. “As a woman, I’m going to be participating very loudly,” said Capito, who attended Tuesday’s working-group meeting even though she is not a member.

Sens. Susan Collins (R-Maine) and Lisa Murkowski (R-Alaska), in particular, could become thorns in negotiations, in part because of their desire to restore funding for Planned Parenthood, which the House proposal would gut.

Senate Majority Leader Mitch McConnell (R-Ky.), center, grew visibly frustrated Tuesday with questions from reporters about why there were no women in the working group. (Aaron P. Bernstein/Reuters)

In an interview, Collins, a leading centrist, said she is pushing to make health-care negotiations bipartisan within the Senate. In addition to including Democrats, Collins said she has invited Sen. Bill Cassidy (R-La.), another Republican who has expressed concerns about the House bill.

“I’m already having those discussions,” Collins said. “Bill Cassidy is a physician. You would have thought he’d be included. I’m working with him on legislation, and I’m talking with Democrats.”

Sen. Rand Paul (R-Ky.), who is fresh off winning reelection and has been willing to buck party leaders in the past, is also not in the working group. Paul has criticized the House bill for being less than a full repeal and replacement of the Affordable Care Act. Many of his colleagues privately say they expect him to vote no.

In addition, Republican senators from states that expanded Medicaid have held their own meetings in which GOP leadership has also participated.

Senate Majority Leader Mitch McConnell (R-Ky.) and Majority Whip John Cornyn (R-Tex.) grew visibly frustrated Tuesday with questions from reporters about why there were no women in the working group. They sought to de-emphasize that organization as one of many tackling health care in the Senate.

McConnell said that, in addition to the smaller gathering, the discussion in Tuesday’s regularly scheduled lunch for all Republican senators was also almost entirely about health care. Such lunches, open to the broader Senate GOP, are likely to continue to be focused on health care in the weeks ahead, he added.

“The working group that counts is all 52 of us, and we’re having extensive meetings,” McConnell said.

With that narrow advantage in the Senate and under the assumption that all Democrats will align against them, Republicans can lose only two of their own votes and still pass a health-care bill (with a tiebreaking vote from Vice President Pence).

Senate Democrats, meanwhile, penned a letter to GOP leaders Tuesday urging them “drop the current partisan effort to repeal and replace health care reform through reconciliation” and find common aims to work on together, including lowering the cost of prescription drugs.

Cruz’s group began with six members and quickly started meeting, according to four Republicans familiar with the group’s discussions who spoke on the condition of anonymity. By early May, as the House revived and passed its legislation, Cruz had forged an unlikely bond with a fellow member, Sen. Lamar Alexander (R-Tenn.), a Senate veteran and close McConnell ally.

The pair went to McConnell and said they would like to expand the working group as the House legislation headed to the Senate. McConnell agreed, and instead of meeting at Cruz’s office as a klatch, the expanded circle started to meet in McConnell’s suite, which it did again Tuesday, the people said.

Observers say there is an advantage for McConnell in trying to keep Cruz and his allies close to the process, where they may be more likely to accept compromise.

“McConnell recognizes that it’s better to have Cruz and Lee on the inside and not on the outside criticizing,” said James C. Capretta, a resident fellow at the conservative American Enterprise Institute who has briefed congressional Republicans on health care for years. “He views them as ‘have to have’ senators because of the size of the majority.”

This week, Cruz resisted setting specific guidelines on what needs to be in the final Senate product to secure his support. Asked Monday whether he would accept anything less than the regulatory waivers in the House bill, Cruz said, “I don’t think it’s productive to be drawing lines and ultimatums during the conversations.”

Compared with Cruz’s past efforts in the Senate, which have regularly antagonized fellow Republicans, the initial working group was more inclusive. In addition to Alexander, Lee, Portman and Gardner, it also involved Sen. Tom Cotton (R-Ark.), who is grappling with the demands of representing a state that leans heavily to the right but has dramatically lowered its uninsured rate under Obamacare.

The group also includes the heads of the Budget and Finance Committees, Sens. Mike Enzi (R-Wyo.) and Orrin G. Hatch (R-Utah), as well as Republican Policy Committee Chairman John Barrasso (Wyo.) and Sen. Patrick J. Toomey (Pa.).

“We’re going to take the time we need to get it right,” Alexander, who heads the Health, Education, Labor and Pensions Committee, said this week when asked whether the White House was pressuring him and others to move swiftly.

Among other things, they must wait for a report on the House measure from the nonpartisan Congressional Budget Office, which will estimate the legislation’s impact on the deficit and project how many people stand to lose coverage.

Those details could take several weeks to obtain. Then, Republicans will be looking for a judgment call from the nonpartisan Senate parliamentarian about whether any elements of the House bill must be struck to allow a procedural maneuver that enables fiscal-related legislation to be passed with a simple majority. That, in turn, would allow them to avoid the 60-vote threshold — requiring Democratic votes — that most legislation must clear.

Cruz has also been communicating daily with members of the hard-right House Freedom Caucus, which heavily influenced the House bill, according to two people close to the group. He updates them on Senate discussions — a relationship that has made some of Cruz’s colleagues uneasy, since they see the Freedom Caucus as unreliable and too far right in its positioning.

Adding to the uncertainty: Some senators are just now jumping into the talks in earnest.

“I think we’ve had total of one meeting so far,” Toomey said Monday. “Have I missed one?”