WASHINGTON — Senate Majority Leader Mitch McConnell is aiming to send a revised version of his health-care bill to the Congressional Budget Office as soon as Friday as he continues to push for a vote before Congress’s August recess.

The effort reflects the tight timeline McConnell faces in his attempt to hold a vote in July — and the pressure he is under to change the bill to garner enough support to pass it. With both conservatives and centrists pushing different policy solutions, Senate leaders were struggling to craft a rewrite of the Affordable Care Act on Wednesday that would attract votes without torpedoing the CBO’s official score of how the legislation affects coverage levels and federal spending.

In between closed-door lunches and meetings with McConnell and his team on Wednesday, a number of Republicans flashed visible signs of frustration even as they expressed cautious optimism that a vote was possible. Conservatives asked for the lifting of coverage mandates to lower premiums and requested higher limits on tax exemptions for health-savings accounts. Moderates asked for more generous tax credits for the working classes and a gentler phaseout of the expansion of Medicaid that their states have enjoyed under the Affordable Care Act.

Some members questioned McConnell’s handling of the issue — an unusual public rebuke of a leader who managed to preserve his party’s control of the upper chamber despite a stiff challenge from Democrats in last year’s elections.

“This has been way more difficult than it needs to be,” said Sen. Ron Johnson, R-Wis., who was among five senators whose opposition to the bill prompted McConnell to postpone a vote this week.

With Vice President Mike Pence prepared to cast the tiebreaking vote, and all Democrats opposed to repealing the 2010 law known as Obamacare, Republicans need the support of all but two of their 52 senators.

The draft bill that stalled this week would cut $772 billion from the nation’s Medicaid program over the next decade, by phasing out the program’s expansion under the ACA and reining in spending on the overall program, especially starting in 2025. It would also repeal or delay $541 billion in taxes, primarily on wealthy Americans and insurers.

The move to cut Medicaid, which covers nearly 70 million Americans, helps offset the bill’s generous tax cuts. But it has generated significant opposition among more than a half-dozen centrists who fear the reductions will impede the nation’s effort to address the opioid crisis and could leave many vulnerable Americans without any health coverage at all.

McConnell spent most of the afternoon in closed-door talks with GOP moderates who appear open to negotiation. The revolving door of meetings included Sens. Dean Heller (Nev.), Shelley Moore Capito (W.Va.) and Bob Corker (Tenn.) along with Alaska’s two senators, Lisa Murkowski and Dan Sullivan, and Sen. Tom Cotton (Ark.).

“It is important to me that lower-income citizens have the ability to actually purchase plans that insure them and give them health care,” Corker said after his meeting with McConnell. “My hope is and my belief is that it is going to be addressed.”

President Donald Trump, meanwhile, questioned in a tweet Wednesday afternoon why some were complaining about the bill’s impact on the long-standing entitlement program.

“Democrats purposely misstated Medicaid under new Senate bill — actually goes up,” he tweeted.

The tweet included a chart showing that, after a downturn in the early 2020s, federal expenditures on Medicaid would increase in absolute terms under the Senate bill. The chart excluded another trend line, part of the Congressional Budget Office’s recent analysis of the bill, showing that the legislation would result in nearly $800 billion less spent on Medicaid over the coming decade than if the ACA stays in place.

While the legislation is likely to undergo further revisions after this next update, McConnell is trying to move quickly to produce a new CBO score by the time lawmakers return to Washington in mid-July. That would give the Senate about two weeks to fulfill the majority leader’s goal of voting before the August recess.

McConnell and his aides plan to continue negotiations through the end of the week and will be in frequent communication with the CBO, according to McConnell spokesman David Popp.

The majority leader needs to bring on board about nine senators who have said they wouldn’t vote for the Better Care Reconciliation Act in its current form. Moving to the left could mollify the moderates from states that expanded Medicaid, while moving to the right would appease conservatives in the Senate — but also in the House, where any Senate bill would also have to pass.

One Capitol Hill aide described the situation as akin to the weeks leading up to the draft bill’s release, when McConnell presented chunks of the emerging legislation to the CBO to expedite the scoring process.

In a sign of how McConnell has only intensified negotiations in the past 24 hours, he huddled Wednesday afternoon at length with Heller and Capito, two Republican senators who have complained loudly that the proposal cuts Medicaid too deeply.

Heller left a weekly strategy lunch Wednesday and walked directly into McConnell’s private office in the Capitol. The two met for nearly 45 minutes, eventually being joined by Capito. Heller darted out a back entrance and down a private hallway, evading reporters.

The activity followed a dramatic day on the Hill on Tuesday, when Republican leaders bowed to pressure from within their ranks and postponed a vote until after the Fourth of July recess. The move bought Republican leaders more time to work out disagreements but also gave rise to new doubts about their ability to bring the matter to a final vote.

Trump is trying to help, mainly by wooing skeptical conservatives, which he has struggled to do. He convened a meeting of all GOP senators at the White House on Tuesday after McConnell announced that the vote would be delayed.

But the White House appears less involved in crafting specific policy tweaks. From the outset of the effort, McConnell and a small clutch of aides have controlled that process.

GOP leaders are exploring whether they can use some of the nearly $200 billion that the CBO has determined they can spend without violating Senate budget rules to address the priorities of the bill’s conservative and centrist critics.

Among the specific changes discussed Wednesday were an increase in the savings limits for health-savings accounts, more generous tax credits for lower- and middle-class earners, and a gradual step-down for people near the higher income threshold for Medicaid, according to senators and aides who spoke on the condition of anonymity to discuss ongoing negotiations.

Senators also proposed a more generous growth rate for Medicaid reimbursements after federal spending in the program was changed from an open-ended entitlement to a per-person cap. Under the current draft, starting in 2025 the federal government would apply the consumer price index for urban consumers, a lower inflation rate, to Medicaid payments.

Sen. Ted Cruz, R-Texas, a conservative who helped shut down the government in 2013 in an effort to repeal Obamacare, continued to call for fewer restrictions on the types of plans that can be offered. Cruz wants to allow insurers to offer bare-bones plans that do not meet minimum requirements, such as providing protections against charging higher rates for preexisting conditions, as long as they also offer at least one fully loaded option.

“What that does is it maintains the existing protections but it gives consumers additional new options above and beyond what they can purchase today,” Cruz told reporters. “That would have the effect of significantly lowering premiums and allowing more people to afford to buy insurance plans.”

Centrists such as Sen. Bill Cassidy, R-La., worry that Cruz’s plan would cause a domino effect that would destabilize risk pools across the insurance market and create unfairly high pricing, particularly for women who need maternity care.

“Yes, you want cheaper plans, absolutely,” Cassidy said. “Unless you have a common risk pool, you end up with policies that don’t cover maternity. As best I tell, women don’t get pregnant without sperm.”

Cassidy called it an “existential question” when asked whether the legislation was back on track. “I can’t speak for the leader,” he said. “It’s the leader’s staff that’s drafting this.”

The Washington Post’s Paige Winfield Cunningham, Paul Kane, David Weigel Elise Viebeck, Robert Costa and Amy Goldstein.

Senate Majority Leader Mitch McConnell of Kentucky, left, and Senate Majority Whip Sen. John Cornyn, R-Texas, speak with reporters outside of the White House after they and other Senate Republicans had a meeting with President Trump on Tuesday.