WASHINGTON — Senate Republican leaders bowed to pressure from within their own ranks Tuesday and postponed a vote to overhaul the Affordable Care Act until after the July 4 recess, raising doubts about their ability to fulfill one of their party’s core political promises.

The delay, which now exposes lawmakers to a barrage of lobbying as they face their constituents over the holiday, has left a measure orchestrated to pass swiftly this week now teetering in the balance. But Senate Majority Leader Mitch McConnell, R-Ky., had little choice after five Senate Republicans, including Sen. Susan Collins of Maine, said they could not support a move to bring up the bill this week in the wake of a new budget analysis of the bill’s impacts.

Conservatives are blasting the plan for leaving too much of the existing law in place, while a coalition of patient advocates, doctors and senior citizens’ groups have joined Democrats in decrying its proposed cuts to the Medicaid program and rollback of taxes imposed on the wealthy.

Speaking to reporters Tuesday, McConnell said leaders were “still working to get 50 people in a more comfortable place” on what he described as “a very complicated subject.”

“But we’re going to press on,” he said. “We think the status quo is unsustainable.”

Republican leaders, who had sought to pass legislation they just released Thursday within a few days so the House could take it up and send it to President Trump before the Fourth of July break, are now bracing for attacks from both ends of the political spectrum.

On Tuesday, Club for Growth President David McIntosh, who has clashed with Republican Party leaders in the past, issued a statement saying the proposal “restores Obamacare.”

“Only in Washington does repeal translate to restore,” McIntosh said. “And while it’s hard to imagine, in some ways the Senate’s legislation would make our nation’s failing health-care system worse.”

Meanwhile, progressive groups began laying the groundwork to attend senators’ public events, while medical providers and groups representing Americans with chronic illnesses predicted that the bill could leave millions without access to adequate medical care. The Congressional Budget Office concluded Monday that the measure would cause an estimated 22 million more Americans to be uninsured by the end of the coming decade while reducing federal spending by $321 billion.

Atul Grover, executive vice president of the Association of American Medical Colleges, told reporters that he and other doctors “take it personally” that the bill would lock people out of insurance for six months if they go for 63 days without a health plan and try to sign up for one the next year.

“We’re there at the bedside,” Grover said, adding that none of his members would be willing to tell a patient: “I’m sorry about your stage-four cancer. Come back in six months, when your insurance kicks in.”

In the wake of the setback, Trump invited Republican senators to meet with him in the White House’s East Room to discuss next steps. With Vice President Mike Pence ready to cast a tiebreaking vote on the measure, Republican leaders can lose only two of their 52 members to pass the bill, which no Democrat is willing to support.

Sitting between two of the bill’s holdouts – Sens. Lisa Murkowski of Alaska and Maine’s Collins – the president said Republicans are “getting very close” to securing the votes they need even as he acknowledged that they might fail.

“This will be great if we get it done,” Trump said. “And if we don’t get it done, it’s just going to be something that we’re not going to like – and that’s OK. I understand that very well.”

Members who publicly opposed the bill had faced a full-court lobbying press from party leaders, but resisted it anyway. Within the past two and a half days, Sen. Ron Johnson, of Wisconsin, has spoken with Trump, Pence, Health and Human Services Secretary Tom Price and House Speaker Paul Ryan, of Wisconsin. Sen. Rand Paul, R-Ky., spoke by phone with Trump on Monday and was scheduled to meet with him Tuesday before the vote was scuttled.

Johnson said he was “grateful” that the vote was postponed, adding that the “real deadline” would arrive when the ACA insurance markets collapse.

But other Republicans, such as Sen. Patrick Toomey, of Pennsylvania, acknowledged that the delay could just as easily jeopardize the bill’s prospects. More time, Toomey said, “could be good and it could be bad.”

Organizers at numerous “Resistance” groups, chastened by their premature celebrations after the House’s repeal push seemed to stall, said that they’d use the recess to ramp up public pressure on Republicans. CREDO Action, which had organized 45,000 phone calls to Senate offices, planned to increase that number when senators went home. NARAL, Planned Parenthood, MoveOn and Daily Action were organizing their own phone banks, while Indivisible groups were organizing visits – and perhaps sit-ins – at local offices.

All of that would supplement under-the-radar but attention-grabbing TV ad campaigns from AARP, Protect Our Care and other progressive and industry groups. The goal, said activists, is to educate voters and break through to local media, which had not often put the development of the Senate bill on front pages or newscasts.

Senate Minority Leader Charles Schumer, D-N.Y., said that while “the fight is not over,” he was confident that Republicans would not succeed because their proposals remain unpopular with the public.

“The Republican bill is rotten at the core,” Schumer said. “We have a darn good chance of defeating it, a week from now, a month from now, a year from now.”

Senate leaders had been working with undecided senators to determine whether any skeptics could be won over with additional spending on priorities such as expanding incentives for health-savings accounts favored by conservatives or a fund to help battle opioid addiction favored by Sens. Rob Portman, R-Ohio, and Shelley Moore Capito, R-W.Va. Leaders can spend about $188 billion on increased spending without running afoul of Senate budget rules.

But as of Tuesday afternoon, the leaders had not earned the votes of the two members, who put out a joint statement in opposition to the current proposal.

“As drafted, this bill will not ensure access to affordable health care in West Virginia, does not do enough to combat the opioid epidemic that is devastating my state, cuts traditional Medicaid too deeply, and harms rural health care providers,” Capito said.

In a sign of how pervasive opposition to McConnell’s plan was, Sen. Jerry Moran, R-Kan., usually a reliable Republican vote, tweeted after the bill was delayed: “The Senate health care bill missed the mark for Kansans and therefore did not have my support.”

Senate leaders had hoped to salvage the effort by using the CBO’s estimates of deficit savings to allocate additional funds to try to ease some members’ concerns.

But the release of the 49-page CBO report late Monday afternoon provided a formidable hurdle for the bill. No new senators immediately said they would back the legislation, and Sens. Johnson, Paul, Collins, and Mike Lee, of Utah, signaled that they would vote against starting debate on the bill in its current form. A fifth senator, Dean Heller, R-Nev., had expressed his opposition last week and has not shown subsequent signs of changing his mind.

Collins, a moderate Republican, tweeted that the measure would “hurt the most vulnerable Americans” and failed to solve the problems of access to care in rural Maine, where, she wrote, “hospitals are already struggling.”

Several Republican senators said they devoted the bulk of Tuesday’s lunch to questioning representatives from the CBO on their methods and estimates. Senators complained that the estimates provided in Monday’s reports used old data about how many people were covered through Obamacare and how much their coverage cost. Others asked that CBO analysts begin the process over with fresh numbers.

“They’re using the March 2016 insurance market,” said Sen. Roy Blunt, R-Mo. “A lot of what they do is just guessing.”

The CBO estimated that two-thirds of the drop in health coverage a decade from now would fall on low-income people who rely on Medicaid. And among the millions now buying private health plans through ACA marketplaces, the biggest losers would roughly parallel those under legislation passed recently by the House: The sharpest spike in insurance premiums would fall on middle-age and somewhat older Americans.

According to the latest report, the Senate bill would mean that an estimated 15 million fewer Americans would have coverage next year, compared with the number if the ACA, commonly called Obamacare, remained in place. At the end of the decade, the 22 million increase in the ranks of the uninsured would include 15 million low-income Americans who would otherwise be on Medicaid and 7 million with private insurance.

That figure, about 1 million less than the House bill, would be equivalent to all the residents in 16 states – Kansas, New Mexico, Nebraska, West Virginia, Idaho, Hawaii, New Hampshire, Maine, Rhode Island, Montana, Delaware, South Dakota, North Dakota, Alaska, Vermont and Wyoming – losing health coverage.