By Sean Sullivan, Juliet Eilperin, Kelsey Snell

US Senate Majority Leader Mitch McConnell is aiming to send a revised version of his healthcare bill to the Congressional Budget Office as soon as Saturday 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 make changes to the bill that will garner enough support to pass.

With both conservatives and centrists pushing different policy solutions, Senate leaders were still struggling to craft a rewrite of the Affordable Care Act that would attract votes without torpedoing the CBO's official score of how the legislation affects coverage levels and federal spending.

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In between closed-door lunches and meetings with McConnell and his team, a number of Republicans flashed visible signs of of frustration even as they expressed reluctant optimism that a vote was still possible.

"This has been way more difficult than it needs to be," said Senator Ron Johnson, who was among five senators whose opposition to the bill prompted McConnell to postpone a vote this week. "I'm doing everything I can to discipline a problem-solving process."

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 would cut US$772 billion from the nation's Medicaid programme over the next decade, along with reducing federal payments further by applying a lower inflation rate to federal reimbursements starting in 2025.

It would also repeal or delay US$541b in taxes, primarily on wealthy Americans and insurers.

Senator Bill Cassidy, one of more than half a dozen GOP senators who have raised concerns on the impact of proposed Medicaid cuts in their states, said that it remained impossible to predict if a refashioned bill could change enough members' minds.

"That is an existential question, and it's very hard for me to answer existential questions," Cassidy said.

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.

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That would give the Senate about two weeks to fulfill the majority leader's goal of voting before the August recess.

Senator Rand Paul suggested that Republicans hope to strike a new agreement by August 1.