Washington (CNN) After Senate Majority Leader Mitch McConnell announced he would postpone a vote on a bill to repeal Obamacare, a group of stunned Republican lawmakers went to the White House Tuesday afternoon to air their grievances -- and chart a path forward -- with President Donald Trump.

Senators expressed concerns about different aspects of the bill, including lawmakers from states expanding Medicaid, conservatives raising concerns about elements of the bill, and others about the tax cuts to the wealthy paired with cuts to Medicaid, a source in the room said.

Multiple senators also relayed a message: Ads from a conservative group against moderate GOP Sen. Dean Heller of Nevada for not embracing the health care bill aren't helping. Heller himself raised the issue with Trump, a source said. Heller also joked that he was really disappointed that they used Matt Damon's face instead of his in the ad, a source familiar with his remarks said, which drew laughs from the President and others in the the room.

Still, the discussion, several senators said, was positive, constructive and not tense -- a change from the last 10 days leading up to what was expected to be a vote on the bill later this week.

For weeks, Republicans have been publicly and privately admonishing the way their health care bill was crafted. Many accused leadership of moving too quickly. Others criticized the fact the Senate hadn't held a single hearing on the bill. But, Tuesday's announcement was still a rare setback for McConnell -- an applauded Senate tactician -- who has pushed his party to fall in line countless times before.

But after years of promising to repeal Obamacare on the campaign trail, it was five Republican senators this week who blocked the bill from even coming to the Senate floor for debate.

"Look, there's more work that needs to be done. I think it's pretty obvious at this point," Idaho Republican Jim Risch said. "If there's more work to be done, you shouldn't try to light the fire before it's ready to be lit."

McConnell's announcement to delay the vote came less than a day after the nonpartisan Congressional Budget Office announced that 22 million more Americans would be uninsured over the next decade if the Republican Senate bill passed. That news alone had caused some Republicans to want to take a step back and get more questions answered.

"I'll just speak for myself. I mean, I'm reading the CBO report at 4 a.m. It came out yesterday afternoon. I was busy until late last night," said Sen. Bob Corker, R-Tennessee. "Not frustration, but you know that there's almost no way for the questions that you have to be legitimately answered."

JUST WATCHED Collins: Tinkering won't fix Senate bill Replay More Videos ... MUST WATCH Collins: Tinkering won't fix Senate bill 01:19

At the White House, Trump proclaimed the bill was still on its way to completion because of the need to repeal the Affordable Care Act.

"For the country, we have to have health care and it can't be Obamacare, which is melting down," Trump said before the closed-door session. "This will be great if we get it done, and if we don't get it done it is just going to be something we aren't going to like. And that is OK and I understand that very well."

The extra time will be appreciated by nervous senators.

"The good thing is, we're not voting this week," said Alaska Sen. Lisa Murkowski, who has expressed concerns about the legislation but so far declined to say whether she would vote for a motion to proceed.

"I truly appreciate the fact that we have more time," Sen. Ron Johnson, a Republican who'd already said he wouldn't vote for the current version of the bill, said as he left a senators lunch Tuesday. "This is a difficult, difficult process."

McConnell's decision was so last-minute that even senior Senate Republicans appeared unaware that the announcement was coming.

Texas Sen. John Cornyn, the Senate GOP Whip, insisted to reporters before the Tuesday luncheon got underway that the procedural vote would take place "tomorrow sometime."

But as he left the gathering, Cornyn conceded: "We need more time."

"It's a conversation and we haven't finished our conversation," he said.

Republicans over the weekend had been scrambling to reach out to their state officials and try to analyze the effect the Senate health care bill was going to have.

Corker insisted that McConnell's decision to delay the health care vote had been his alone.

"It was Mitch's... Definitely Mitch," Corker said.

JUST WATCHED Kasich: People are 'fed up' with health care partisanship Replay More Videos ... MUST WATCH Kasich: People are 'fed up' with health care partisanship 04:59

Still work to do

Now, the hard work continues.

Despite clear signs that lawmakers were breathing sighs of relief, McConnell's challenge of reaching 50 "yes" votes remains monumental.

After McConnell announced the vote was delayed, more Republican senators publicly came out against the current version of the bill. Sen. Jerry Moran -- a former Chairman of the National Republican Senatorial Committee and close ally to leadership -- tweeted "The Senate healthcare bill missed the mark for Kansans and therefore did not have my support."

Sens. Rob Portman of Ohio and Shelley Moore Capito of West Virginia announced in a joint statement Tuesday afternoon that they were opposed to the Senate health care bill, bringing up the total tally of "no" votes to nine.

"I continue to have real concerns about the Medicaid policies in this bill, especially those that impact drug treatment at a time when Ohio is facing an opioid epidemic," Portman said.

Capito -- one of the senators that Trump called over the weekend -- said that the legislation would "will not ensure access to affordable health care in West Virginia, does not do enough to combat the opioid epidemic that is devastating my state, cuts traditional Medicaid too deeply, and harms rural health care providers."

Meanwhile, other critics of the bill signaled that winning them over would take a lot more than just minor fixes.

"I have so many fundamental problems with the bill that have been confirmed by the CBO report that it's difficult for me to see how any tinkering is going to satisfy my fundamental and deep concerns about the impact of the bill," said Maine GOP Sen. Susan Collins.

Sen. Rand Paul, who has opposed the current bill, said he thought Trump wanted to improve the bill.

"He understands that he's got people coming from all different directions within the Republican caucus, and it's going to take some work," Paul said on CNN's "Erin Burnett OutFront," adding he and other conservatives sent written proposals to the White House to change the bill.

Democrats cautious after House experience

Senate Democrats hardly celebrated the news of the vote delay. In fact, they pointed to what happened to House Speaker Paul Ryan, who was forced in March to yank his health care bill from the House floor when there wasn't enough support, as a telling lesson.

After weeks of tense negotiations and changes to the bill, Ryan was able to bring the legislation back -- and narrowly get it through the House.

Democratic Sen. Patty Murray warned Tuesday that the desire among Republicans to overhaul Obamacare remained as strong as ever.

"We don't know what kinds of backroom deals Senate Republican leaders will cut," Murray said. "But here's what we do know: Sen. McConnell is not going to give up. He wants to get to yes."

Democratic Sen. Richard Blumenthal of Connecticut told CNN it was only a "temporary victory."

"We were as much somber as celebratory because we know we're going to have a fight when we get back."