Senate Majority Leader Mitch McConnell's latest attempt to make good on the GOP's seven-year campaign promise to gut the Affordable Care Act was once again plunged into chaos Tuesday when three Republican senators said they would oppose a procedural vote to advance McConnell's plan to roll back significant parts of Obamacare without a replacement plan in place.

For the second time in a span of less than 24 hours, McConnell acknowledged that things were not going as he had hoped.

Despite not having the votes for passage, McConnell announced Tuesday night on the Senate floor that Republicans would hold a procedural vote on the health care bill "early next week."

Asked by CNN what would need to change given that leadership currently lacks the 50 "yes" votes from senators to pass even a procedural vote, Senate GOP whip John Cornyn responded: "A little passage of time."

The opposition that trickled out into the public Tuesday reinforced a painful reality for many Republicans to swallow -- that after years of railing against Obamacare, there is now not enough will within the party to pursue wholesale repeal of the law.

In short order, Sens. Lisa Murkowski of Alaska, Shelley Moore Capito of West Virginia and Susan Collins of Maine said they oppose McConnell's proposal.

"My position on this issue is driven by its impact on West Virginians," Capito said in a statement. "With that in mind, I cannot vote to repeal Obamacare without a replacement plan that addresses my concerns and the needs of West Virginians."

She later tweeted she would not vote to move forward on a motion to proceed to repeal Obamacare without a replacement.

Murkowski called for Republicans to develop a new proposal in committees, a step that has thus far been skipped by GOP leadership in the chamber.

"I think what has to happen is the Republicans have to admit that some of the things in the ACA, we actually liked, and the Democrats have to admit that some of the things they voted for in the ACA are broken and need to be fixed," Murkowski told reporters.

McConnell was forced to concede Monday night that his original attempt to repeal and replace the health care law at the same time was no longer a viable strategy, and he proposed that the Senate move ahead with a vote to take up an Obamacare repeal bill that the House passed earlier this year and aim to introduce as an amendment to the 2015 bill that would effectively roll back key parts of Obamacare after a two-year waiting period. That legislation was approved by a GOP-controlled Congress at the time but vetoed by then-President Barack Obama.

Republican senators were skittish enough that their health care bill would leave 22 million people more without health insurance by 2026, compared to Obamacare.

Repealing without a replacement plan in hand would probably leave 18 million more people without coverage in the first year after its enactment and 32 million more by 2026, according to a Congressional Budget Office report that looked at an earlier GOP bill to repeal Obamacare.

It would also cause premiums on individual market policies to increase by up to 25% the first year and to nearly double by 2026.

'Let Obamacare fail'

Meanwhile, the pressure continued to come from the White House.

Amid the news of McConnell's latest defeat, President Donald Trump told reporters during a luncheon with Afghanistan veterans at the White House that he was "very disappointed" by Senate Republican's inability to pass health care. He added that his new plan is to "let Obamacare fail and then the Democrats are going to come to us."

Even still, Trump said Tuesday that he doesn't think the Republican plan "is dead" but it "may not be as quick as we had hoped but it is going to happen."

White House deputy press secretary Sarah Huckabee Sanders told reporters that the White House's message to Congress is "do their job."

"At this point, inaction is not a workable solution so they need to come to the table and figure out how to reform the system and fix it," she said.

The weight of the most recent development quickly cast a shadow over Republicans on Capitol Hill Tuesday afternoon.

Sen. Ron Johnson, a Wisconsin Republican and a key vote, reflected that it might be time for Republicans to move on from repealing and replacing Obamacare "pretty quickly."

"I think we need to move on probably pretty quickly," Johnson said. "I mean, we've been at this. It did not, unfortunately, end in success."

Meanwhile, with some GOP lawmakers' key priorities like boosting funding for the opioid crisis now also stalled, Republicans who were planning to vote for the Senate health care bill are looking at their colleagues bewildered by the latest state of play.

"It was not the best possible bill, but it was the best bill possible," said Sen. Pat Roberts of Kansas. "When you can't even get to a motion to proceed, you're in pretty bad shape."

Asked what it said about the Republican Party's ability to govern, Roberts candidly replied "not much."

After the chaos of Tuesday, Sen. Lamar Alexander, the Senate's health committee chairman, acknowledged that it was time for Republicans to open up the process. He announced that his committee would begin holding hearings on how to stabilize the health care market -- an area that enjoys potential bipartisan cooperation.

"However the votes come out on the health care bill, the Senate health committee has a responsibility during the next few weeks to hold hearings to continue exploring how to stabilize the individual market," Alexander said in a statement. "I will consult with Senate leadership and then I will set those hearings after the Senate votes on the health care bill."