Senate Majority Leader Mitch McConnell with President Donald Trump. Evan Vucci/AP Images

The Senate Republican healthcare bill teetered on the brink of collapse on Tuesday morning, just a few days after it was unveiled and the morning after the Congressional Budget Office delivered a brutal assessment of its potential effects on coverage.

Sen. Susan Collins of Maine, a key moderate vote in the Republican conference, tweeted on Monday night that given its potential effects, she would not vote for the legislation — or even a motion to move it forward on the Senate floor.

"I want to work w/ my GOP & Dem colleagues to fix the flaws in ACA. CBO analysis shows Senate bill won't do it," Collins tweeted Monday, adding that she would "vote no" on a motion to proceed.

Other members of the GOP Senate conference also appear to be on the fence about voting for the legislation, officially named the Better Care Reconciliation Act. Many of them wavered after an analysis from the nonpartisan CBO released Monday predicted that the BCRA would reduce the number of insured Americans by 22 million in 2026 compared with the current baseline.

Sen. Ron Johnson, of Wisconsin, one of four conservatives who came out against the legislation when it was released last week, also said on Monday that he had "a hard time believing I'll have enough information for me to support a motion to proceed this week."

A representative for Sen. Mike Lee, another conservative holdout, told The New York Times on Monday that the senator would not vote for the legislation as written.

Collins and Johnson joined Sens. Dean Heller and Rand Paul, who previously announced their opposition to a motion-to-proceed vote for the bill. Any more than two votes by GOP members against the motion would defeat it, as Senate Democrats universally oppose it.

Heller is up for reelection in 2018 in Nevada, a state that Hillary Clinton won and that has a popular GOP governor who opposes the BCRA for its cuts to Medicaid. Heller on Friday announced his intention to vote against the legislation.

In Paul, GOP leaders have the opposite problem, as the Kentucky senator believes the BCRA does not go far enough in its repeal of the Affordable Care Act, the healthcare law better known as Obamacare.

On Monday, moderate Sen. Lisa Murkowski of Alaska said she had not gotten to a "yes" vote yet and wanted to learn more about the bill's potential effects on her state.

"I don't have enough data in terms of the impact to my state to be able to vote in the affirmative," Murkowski told CNN's Dana Bash.

Sen. Bill Cassidy of Louisiana also wavered after seeing the CBO score.

"It makes me more concerned," Cassidy told CNN. "I've been uncommitted and I remain uncommitted — I mean just deadline uncommitted. But it certainly makes me more concerned and makes me want to explore this more."

Republican Sen. Susan Collins of Maine. Associated Press/Evan Vucci

Republican leadership targeted a vote late Tuesday or early Wednesday on the motion to proceed to get a final vote by the end of the week. This plan would finish the process before the weeklong July 4 congressional recess.

Senate GOP leadership had not given up hope as of Monday night, seeking to alleviate members’ concerns and at the very least clear the motion to proceed.

"We're trying to accommodate their concerns without losing other support," Senate Majority Whip John Cornyn told reporters, adding the conference was in a "good place."

The White House is also attempting to exert its influence on the process, with Vice President Mike Pence dining with conservative members of the caucus including Lee, who signed a letter opposing the bill on Thursday.

President Donald Trump called Cruz, Johnson, Paul, and Sen. Shelley Moore Capito of West Virginia to ask for their support on the bill, according to the White House press secretary, Sean Spicer.

But Trump himself has wavered over the past several weeks. In an interview that aired Sunday, he appeared to confirm to Fox News that he called the House's version of the healthcare bill "mean." His comments have been a constant point of attack for Democrats over the past week.

The mix of members opposing the motion leaves leadership in a precarious position. If Senate leaders try to move the bill to the right by cutting more funding or repealing regulations to appease conservatives like Lee, Paul, and Johnson, they could further alienate Collins and Heller, as well as Murkowski and Capito.

Move the bill to center with more generous funding, a smaller deficit reduction, and a slower phasing out of Obamacare's Medicaid expansion, and Lee, Johnson, Paul, and Cruz could block the vote.

But as many longtime political observers suggested Monday, Senate Majority Leader Mitch McConnell would be as capable as anyone of brokering a deal that would placate both wings of the party.

Still, a deal is "unlikely before the end of this week, when the July 4 break begins — it's not even certain a motion to proceed can pass today or tomorrow," said Greg Valliere, the chief strategist at Horizon Investments. "But McConnell now has an option — he can yank the bill this week, delaying a final vote until late July, giving him time for wheeling and dealing with individual members."