The Republican senators who have been the most critical of their party’s tax overhaul plan came out of a lunch meeting with President Trump Tuesday sounding more like yes votes, telling reporters that Trump promised many of them he’d back the various policy changes they want to see in the bill.

Key former hold-outs like Sens. Susan Collins (R-ME), Ron Johnson (R-WI) and Bob Corker (R-TN) all exited the meeting sounding significantly more optimistic that they will be able to support the bill, with Collins and Corker both saying Trump promised them support for the changes they want to see.

“A lot of my concerns, it appears, are going to be addressed,” Collins told TPM during a conversation with reporters.

Almost immediately after the lunch, the tax bill sailed through the Senate Budget Committee — something that didn’t seem like a done deal Tuesday morning, when both Corker and Johnson were still suggesting they would vote against it in committee.

Now, the bill to make major corporate tax cuts and gut Obamacare’s individual mandate has significantly more momentum as Republicans rush to try to push it through Congress before the end of the year.

Yet the devil remains in the details, and Trump has made promises before that GOP leaders couldn’t keep. But if Collins gets onboard as well as GOP senators like Corker who are concerned about the bill exploding the national debt and those like Johnson who want even more generous tax cuts for smaller businesses, it’s likely to pass the Senate later this week. Republicans can afford to lose only two of their own members and still pass the bill.

Collins, the most outspoken critic of Republican’s gambit to repeal Obamacare’s individual mandate in the tax bill, said Trump agreed Tuesday to back two bipartisan health care bills to mitigate the harmful effects killing the mandate: one from Sens. Lamar Alexander (R-TN) and Patty Murray (D-WA) to provide money to stabilize insurance markets and another from her and Sen. Bill Nelson (D-FL) to fund a federal reinsurance program.

Alexander confirmed that Trump had offered support for both his health care bill and Collins’.

Collins, though she claimed Tuesday to still be undecided on the overall bill, also appeared to have loosened her demands. Though she said just a few weeks ago that she wanted both health care bills passed before the Senate voted on the tax and mandate repeal bill, she moved the goalpost on Tuesday, telling reporters that they need to pass before the House-Senate conference committee issues its final report.

The Congressional Budget Office estimates that repealing the mandate would increase premiums by more than 10 percent and drive at least 13 million people out of the health insurance market over the next 10 years.

Trump’s promises seem to have won over other hold-outs as well.

The camp of Republican senators wary of the tax bill’s potential to massively increase the deficit also appeared to be mollified by promises secured during the meeting as well.

Corker, who earlier on Tuesday said he’d like to take half the bill “directly to the incinerator,” told reporters that he got a “verbal agreement” from the president and Republican leadership on the trigger he and other lawmakers want in the bill to undo some of the deepest tax cuts if they don’t create economic growth will be included.

“I think we’ve gotten a commitment that puts us in a pretty good place,” he said, declining to reveal what taxes would fall under the trigger and how many years after the bill’s passage they would kick in.

Corker emphasized that Trump hasn’t concerned himself with the how it works, while touting the president’s support for the measure.

“The White House really isn’t so involved in the mechanics of all this, but they understand it’s important to have something that moves us in a different direction if we’re not hitting the numbers,” he said. “The details of this are not something he deals with quite as much.”

Johnson, another former prominent hold-out, told reporters he keeps “getting assurances” his issue with the bill—wanting more generous tax cuts for pass-through corporations—will be “fixed.”

“We all want to get to yes. That’s a good thing,” he said.

Even as the GOP hold-outs made positive noises, Senate Majority Leader Mitch McConnell (R-KY) made it clear the party hasn’t reached a final agreement — and that any changes made to mollify some members may antagonize others.

“It’s a challenging exercise. I think I’m sitting there with a Rubik’s Cube trying to get 50,” he told reporters. “We have a few members who have concerns and we are trying to address them.”