Reince Priebus, the White House chief of staff, said on "Fox News Sunday" that he was expecting the Senate to make "improvements where they need to be made" in the repeal bill passed last week in the House by a vote of 217 to 213. But Senator Lamar Alexander of Tennessee, chairman of the Senate Health Committee and a member of Mr. McConnell's working group, went much further, suggesting the Senate is basically starting afresh.
Ms. Collins agreed. "The Senate is starting from scratch," she said on Sunday.
But Mr. McConnell is likely to find the same tricky dynamic that Speaker Paul D. Ryan found in the difficult weeks it took to get a bill through the House: Any bill that satisfies conservatives like Mr. Cruz and Mr. Lee risks alienating many other senators, including moderates like Ms. Collins and Ms. Murkowski.
And another issue will vex Republican leaders in ways it did not in the House: Medicaid. Senators in both parties from states that have expanded the health care program for the poor have expressed strong misgivings about the House bill, which essentially unravels the expansion.
The omission of Ms. Collins has especially surprised health policy analysts. For several years starting in the late 1980s, Ms. Collins was the top insurance regulator in Maine. Early this year she introduced a bill with Senator Bill Cassidy, Republican of Louisiana, that would give states much more power to reconfigure their health care systems while also preserving consumer protections in the Affordable Care Act. (Mr. Cassidy was also left off the working group.)
Conservatives mocked the Collins-Cassidy proposal, saying its basic offering to the states was that "if you like Obamacare, you can keep Obamacare."
Democrats said the Republicans' failure to include women in the working group showed that they were politically clueless. "It matters to have women at the table - and it matters when they aren't," Senator Patty Murray of Washington said on Twitter.
David Popp, a spokesman for Mr. McConnell, said on Monday that many Republicans were involved in devising a replacement for President Barack Obama's health care law.
"Senators from throughout the conference have been working on solutions," Mr. Popp said. "Those meetings and efforts continue, including chairmen of the relevant committees and leadership. They will continue to have regular updates with the entire conference so the Senate can continue to move expeditiously on the work ahead as it considers the House-passed legislation."
The Republicans' working group includes Mr. McConnell and three other members of the Republican leadership: John Cornyn of Texas, the majority whip; John Thune of South Dakota, the chairman of the Senate Republican Conference; and John Barrasso of Wyoming, the chairman of the Senate Republican Policy Committee, who has been a point man for the party on health care.
The group also includes three committee chairmen: Mr. Alexander; Senator Orrin G. Hatch of Utah, who leads the Finance Committee; and Senator Michael B. Enzi of Wyoming, the head of the Budget Committee.
The other senators on the Republican working group are from states that have expanded Medicaid under the Affordable Care Act: Tom Cotton of Arkansas, Cory Gardner of Colorado, Rob Portman of Ohio and Patrick J. Toomey of Pennsylvania.
The House bill would roll back the expansion of Medicaid, which has provided coverage to about 11 million people. The Congressional Budget Office said the bill's Medicaid changes would save more than $800 billion over 10 years.
Savings would shrink if the Senate allows states to keep some or all of the Medicaid expansion.
Senate Republicans say they will take the time needed to "get it right" as they draft a replacement for the health care law. At the same time, they say that action is urgently needed because insurance companies are scaling back their participation in insurance marketplaces, creating a possibility that some counties will be served by only one insurer, or perhaps by none at all.
"I know this all too well because 34,000 people in the Knoxville, Tenn., area, my home area, are going to have subsidies in 2018 but no insurance to buy with the subsidies unless Congress acts," Mr. Alexander said.