WASHINGTON — The Senate rejected a proposal Wednesday that would have repealed major parts of the Affordable Care Act, but Republican leaders were growing more confident in their chances of passing a more modest overhaul of the health care system later this week.

Republicans appeared to be coalescing around a “skinny repeal” measure that would abolish the individual and employer insurance mandates and perhaps just one tax in an attempt to sustain their seven-year quest to unwind Barack Obama’s health care law. But even if they succeed – and start negotiations with the House – they will face significant obstacles in accomplishing anything more substantial.

Top Republicans such as Sen. John Thune of South Dakota said that although leaders have not yet found “the sweet spot” between conservatives and centrists, they have picked up support for a more modest plan because it did not include deep cuts to Medicaid. Some Republican senators were simply open to any legislation that could keep alive the roller-coaster push for an overhaul.

“We’re edging closer and closer” to getting 50 votes for a bare-bones plan, Thune said. He said leaders were betting that some Republicans who defected on votes this week would feel more pressure to support any bill that emerged from negotiations with the House to face a final vote in the Senate.

“Voting on something at the end of the process when it’s the only train leaving the station . . . I think that’s a different vote for a lot of people,” he said.

SEARCHING FOR SENATE CONSENSUS

More than half-a-dozen centrists from states that expanded Medicaid under the Affordable Care Act objected to the original Senate draft that was considered Tuesday night. It would have cut the program for low-income Americans by $772 billion over 10 years and curtailed its long-term growth rate.

Yet even if Republicans agree on a minimalist plan to alter the ACA, uniting with their House colleagues to enact a bill would be far more challenging. On Wednesday – even before the “skinny repeal” came up for a vote – some House conservatives were calling it untenable.

Rep. Mark Meadows, R-N.C., chairman of the House Freedom Caucus and a key player in negotiating the House-passed bill, told reporters recently that a “skinny repeal” would be “dead on arrival” in the House and that a conference committee would have to be convened to work out a compromise.

Senate Majority Leader Mitch McConnell, R-Ky., looked as though he was making progress earlier in the week after overcoming serious opposition from his rank-and-file members to begin debate on health care, a prospect that seemed dim just last week. President Trump has taken to Twitter and made public statements challenging Senate Republicans to support an overhaul or take ownership of the ACA’s problems.

But in two votes over the past 24 hours, lawmakers rejected differing approaches to rewriting the landmark 2010 law. The open voting process, which is likely to drag on for the rest of the week, has laid bare the fact that Senate Republicans haven’t been able to find a comprehensive replacement for the law they have relentlessly lambasted.

On Wednesday, Republicans lacked answers for how or even whether they can break their gridlock by simply extending their endeavor, but appeared determined to press ahead.

“I think it’s a good idea to start with what we agree on and see how big we can get the bill from there,” said Sen. Rand Paul, R-Ky., who has pushed for a repeal of the law and has repeatedly clashed with Republican leaders.

Sen. Lindsey Graham, R-S.C., said a scaled-back bill “is not a solution to the problem” the American health care system is facing, but that there did not appear to be another immediate option.

BACKING AN IMPERFECT MEASURE

Republican leaders have little room to navigate when it comes to crafting a bill, because just three defections within their ranks will deprive them of the 50 votes they need to pass legislation with the assistance of Vice President Pence, who can cast a tie-breaking vote.

And in the two most important votes the Senate has cast since taking up the legislation, at least 13 percent of Republicans defected to join Democrats in opposition.

“This certainly won’t be easy. Hardly anything in this process has been,” McConnell said Wednesday on the Senate floor.

But Republicans hope that once their members are faced with enacting an imperfect measure or not accomplishing one of their chief legislative goals, they will decide that some progress is better than none.

Meanwhile, the ongoing uncertainty on Capitol Hill sent jitters through the insurance industry.

Joseph Swedish – the chief executive of Anthem, the nation’s second-largest health insurer – said on a conference call to review second-quarter earnings that the company is reassessing its participation on ACA marketplaces for next year.

Anthem has decided to largely withdraw from the markets in three of the 14 states in which it participates, and Swedish said it may stop participating elsewhere unless the markets appear adequately stable.

He cited, in particular, the question of whether Congress and the Trump administration will continue “cost-sharing subsidies” that the ACA provides insurers to help lower-income customers – about 7 million this year – afford deductibles and other out-of-pocket expenses.

DAMAGE FROM ENDING MANDATES

Noting that Anthem’s “2018 market footprint” for selling ACA health plans is not fully decided, Swedish said, “If we aren’t able to gain certainty on some of these items quickly, we do expect that we will need to revise our rate filings to further narrow our level of participation.”

The Blue Cross Blue Shield Association warned that even the “skinny repeal” Republicans now envision could undermine the individual insurance market because it would eliminate the requirement that Americans buy insurance or pay a tax penalty. The measure, which remains subject to negotiation, also would probably eliminate the ACA’s requirement that employers with 50 workers or more provide health coverage, and a medical device tax that generates $19.6 billion in federal revenue over a decade.

“If there is no longer a requirement for everyone to purchase coverage, it is critical that any legislation include strong incentives for people to obtain health insurance and keep it year-round,” Blue Cross Blue Shield Association said in a prepared statement.

A CBO estimate in December projected that repealing the ACA’s individual mandate would leave 15 million Americans uninsured most years and prompt premiums to rise by 20 percent.