Washington (CNN) The Senate Republican health care bill teetered on the edge of collapse Monday evening after the Congressional Budget Office released a devastating report on its impact and multiple Republicans announced they would not vote to advance the legislation.

The mood was tense and chaotic on Capitol Hill moments after the non-partisan agency predicted that the Republican proposal would result in 22 million more people becoming uninsured by 2026 years than under Obamacare.

Senate Republicans, many of whom are still undecided on whether to vote for the bill later this week, struggled to defend the legislation to mobs of reporters who flocked to them for initial reactions.

In a particularly ominous sign for Senate Majority Leader Mitch McConnell, who has decided to move ahead with a vote later this week despite widespread reservations among his colleagues, it was unclear whether he would even have the needed votes to clear an initial procedural hurdle.

Responding to the Republican opposition in the Senate to the current bill, a White House official conceded, "We're right on the threshold" of losing on health care. The official remarked that, should the legislation collapse in the Senate, the White House would simply move on to tax reform, noting there is the potential for some bipartisan support for that effort.

Kentucky Sen. Rand Paul, who opposes the GOP health care bill, told reporters he would vote against the procedural step -- known as a motion to proceed -- if the legislation remained unchanged. Maine Sen. Susan Collins, a moderate who has been deeply critical of the health care bill, took the same position.

"I want to work w/ my GOP & Dem colleagues to fix the flaws in ACA. CBO analysis shows Senate bill won't do it. I will vote no on mtp," Collins wrote on Twitter. (Earlier in the evening, Collins told reporters that the CBO score was "obviously not positive.")

Senate Majority Whip John Cornyn had hinted earlier in the day that the Senate could move on the motion to proceed by Tuesday, but that came before the CBO analysis.

Wisconsin GOP Sen. Ron Johnson, another holdout who has publicly blistered the process by which the Senate bill has moved through the upper chamber, said bluntly that it would be a "mistake" to move forward with the motion to proceed.

"If Leader McConnell says failure is not an option, don't set yourself up for failure would be my advice for the leader," Johnson told reporters.

Republican backers of the bill highlighted what they said is CBO's poor record of predictions.

"The CBO has consistently proven it cannot accurately predict how healthcare legislation will impact insurance coverage," the White House said in a statement.

White House outreach

With the GOP health care process in jeopardy, the White House appeared to be ramping up its outreach to skeptical lawmakers.

President Donald Trump himself spoke with several senators over the weekend, White House spokesman Sean Spicer said Monday. Collins told CNN that White House Chief of Staff Reince Priebus had reached out to her to discuss the issue.

Vice President Mike Pence will host four senators Tuesday night for dinner at the Naval Observatory: Sens. James Lankford, Mike Lee, Ben Sasse and Tom Cotton (Lee has come out against the bill in its current form, while Lankford, Lee and Cotton are undecided).

But it's unclear just how big of a role Trump is playing in the ongoing Senate deliberations. Some Senate Republicans are cautioning that the President may not even back up senators if public opinion on their health care bill flops in upcoming months.

They are pointing to the fact that Trump called the House health care bill "mean" to senators a month after he hosted a celebration in the White House Rose Garden after the bill's passage.

"Here's what I would tell any senator: If you're counting on the President to have your back, you need to watch it," GOP Sen. Lindsey Graham said.

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Changes coming?

With public opposition mounting, GOP leaders may still make more changes to the original draft bill to woo lawmakers who are on the fence. But time is running out for those negotiations.

South Dakota Sen. John Thune, a member of Senate leadership, said something could be added to the bill to assuage conservatives concerns that the bill doesn't repeal enough Obamacare regulations. But he also cautioned that "for the most part, the dimensions of the bill are starting to take shape."

"I think there probably is a way you could address at least some of the issues they've raised," Thune said.

But as McConnell searches for 50 votes, he will be haunted by complicated political dynamics that made passage of a health care bill so difficult in the House earlier this year: Giving concessions to lawmakers on one end of the political spectrum could turn off members of different ideological sway.

This balancing act dogged House Speaker Paul Ryan in his quest to pass an Obamacare repeal bill, even forcing him in March to yank a bill from the House floor.

Ryan, for his part, declined to answer questions when asked about the CBO Monday afternoon.

"You know I don't walk and talk" Ryan replied.

Democrats are gloating

Democrats have been furious about Republican efforts to gut Obamacare, former President Barack Obama's landmark accomplishment. But Monday's CBO report appeared to put some Democrats in a visibly good mood as they watched their GOP colleagues squirm.

As Collins rode the escalator up to Senate votes surrounded by reporters Monday afternoon, she happened to be walking next to Democratic Sen. Al Franken.

When a reporter asked Collins whether she would like to see the legislation slow down, Franken chimed in: "I want to hear this."

Collins responded that she was still reviewing the CBO report, but that "it's obviously not positive."

Franken, to laughter from reporters listening in, quipped: "Very well done."