Senate budget rules require that the final legislation save at least US$133 billion, more than was saved in the House bill, giving senators US$188 billion to make the bill more palatable.
Any extra spending risks alienating conservatives, however, and could threaten a delicate balance McConnell must strike to win votes from at least 50 of the 52 Senate Republicans. And some moderates have said they will decide whether they can support the Better Care Reconciliation Act based on how it will affect Americans who have gained coverage under the ACA during the past few years.
McConnell said that the legislation is an attempt at finding consensus among Republicans on how to fix healthcare. He urged a quick timeline for action but said the bill is still a draft that can still be changed ahead of a final vote.
"The American people need better care right now," McConnell said in a speech on the Senate floor. "This legislation includes the necessary tools to provide it."
Yet Cassidy, who wants to add better protections for people covered under Medicaid, said that the latest changes to the bill have not gone far enough to win his support.
"It makes me more concerned," Cassidy said in an interview on CNN. "I remain uncommitted."
The fresh figures come as President Donald Trump, in a sharp pivot from the praise he initially lavished on the House bill, is urging the Senate to provide Americans more generous help with health insurance.
The President repeated during a TV appearance a word he had used in a private White House lunch earlier this month with a group of GOP senators: that the House's version is "mean".
According to the 49-page report, the immediate increase in the ranks of the uninsured would be slightly larger than under the House version, with an estimated 15 million fewer Americans likely to have coverage in 2018, compared to 14 million in the House bill.
The Senate's bill also would reduce federal spending on subsidies for people who buy individual health insurance policies significantly more than the House's version, cutting spending for tax credits by US$408 billion by 2026.
Despite uncertainties about how the bill's moving parts would play out, the report says: "The amount of federal revenues collected and the amount of spending on Medicaid would almost surely both be lower than under current law. And the number of uninsured people under this legislation would almost surely be greater than under current law."
Democrats immediately seized on the estimates to criticise Republicans for planning a vote on a bill that would force millions to lose insurance coverage and drive up premiums for seniors. Senate Minority Leader Charles Schumer said the bill cannot be fixed despite McConnell's plan to allow senators to make changes before a final vote.
"Republicans would be wise to read it as a giant stop sign," Schumer told reporters. "No matter how the bill changes around the edges, it is fundamentally rotten at the centre."
Though the ACA's expansion of Medicaid would be phased out over a longer period of time than in the House legislation, cuts to the public insurance programme for the poor still would account for by far the largest share of the reduction in federal spending under the Senate bill - US$772 billion over the coming decade.
The CBO has been regarded over its four-decade history as a source of neutral analyses devoid of political agenda. Its current director, Keith Hall, is a conservative economist who served in the Administration of President George W. Bush and was appointed to his current role two years ago by a Republican Congress.