Republicans aiming to reconcile the differences between the Senate and House tax bills are weighing a lower top individual rate to provide relief to wealthy taxpayers losing state and local tax deductions, and offsetting the lost revenue by setting a corporate tax rate higher than the original target of 20 percent, GOP lawmakers said Tuesday night.

Republicans were still exchanging proposals between the chambers Tuesday evening in anticipation of a public conference meeting on the bill Wednesday but claiming progress toward a deal to merge the bills and fix some of the problems that could hurt the odds of final passage.

One such remedy would be a lower top individual tax rate to aid high-income earners in high-tax states who could see tax increases because of the loss of the state and local tax deduction, known as SALT.

“There have been suggestions about how to solve the SALT problem, one of which is to lower the top rate,” said Republican Sen. John Thune of South Dakota, a member of the conference committee.

One way to pay for that change would be to set a corporate rate higher than the 20 percent called for in both the Senate and House bills.

“The rates, both the business level, the corporate level, and the individual level, are issues that are in play,” Thune said. “And, you know, obviously when you make changes that you need to have scored, you need ways to offset some of those.”

The House version of the bill kept the top individual tax rate the same as under current law, at 39.6 percent. The Senate-passed bill set a top individual tax rate of 38.5 percent.

Republicans were weighing lowering that rate to 37 percent and raising the corporate tax rate to 21 percent, according to reports from the Washington Post and other publications.

Yet top negotiators said that, as of Tuesday evening, the details remained fluid.

“I hesitate to give any figures at this point because it’s still being debated,” said Sen. Orrin Hatch, R-Utah, the chairman of the Senate Finance Committee.

None of the options floated Tuesday appeared to pose an immediate risk to flip the votes of any Republicans in the Senate, where they have a majority of just two.

Sen. Susan Collins, a centrist Maine Republican who has said she opposes lowering the top individual rate, said a 37 percent rate would not be a deal breaker for her. “I'm going to wait and look at the entire conference report,” she said.

Lowering the top rate would affect only very high earners, as the top bracket in both bills applies only to married couples earning more than $1 million.

As for the corporate rate, outside free-market groups rallied this week to pressure Republicans to stick to 20 percent, but stopped short of saying that they would pull support from a bill with a higher rate. Likewise, one of the top Senate proponents of sticking to 20 percent declined to prejudge negotiations Tuesday. “I want to look at the whole package,” said Sen. David Perdue, R-Ga. In defense of a 20 percent rate, he said, other countries are likely to lower their corporate tax rates further in the years ahead to retain an advantage against the U.S.

White House legislative director Marc Short also withheld judgment on a higher corporate rate. “If there’s any changes in that, it obviously depends on what you’re getting in exchange for that,” he said in a Fox Business interview. “We’re optimistic that if anything bumps up that there’ll be other tax relief provided elsewhere in the bill.”

Meanwhile, the conference committee’s chairman, Rep. Kevin Brady, issued a call on Fox News to not delay the corporate rate cut by a year, as the Senate did in its bill. “These tax cuts ought to occur now,” he said, later adding, “Why would we delay that? Let’s get that happening in our economy now.”

The Texas lawmaker also said negotiators were making progress toward keeping the corporate alternative minimum tax out of the final bill, after it was inserted into the Senate version at the last minute.

Even as those details had yet to be settled, GOP leaders began to look ahead to final passage. “You’re going to see this bill on the president's desk by Christmas,” said House GOP Whip Steve Scalise, speaking in an interview on Bloomberg. The Louisiana congressman brushed off the uncertainty over the corporate rate, saying that it would be finalized at a rate lower than the world average.

Arkansas Republican Sen. Tom Cotton, speaking on the "Hugh Hewitt Show," said the bill is nearly as good as passed now that it has reached conference. “Having gone through the House and the Senate, it’s hard to see it failing to pass through the conference committee and then go on to the president,” Cotton said. “There’s no real example of that in modern legislative times.”

“The odds greatly favor enactment,” said Ilona Nickels, an expert on the legislative process and former Congressional Research Service researcher, citing the “political imperative” to get the bill to Trump’s desk.

Wednesday’s public meeting, which will be the only one, will be a carefully stage-managed process, with nearly all the real work taking place among GOP leaders offstage. The meeting at the Capitol, though, will provide an opportunity for opponents to stage protests, as liberal groups have planned.

Once the committee has officially filed its report, which leaders said would come this week, there will be pressure for the House and Senate to finalize legislative text and vote next week.

“As soon as they do reach an agreement, we need to go vote, like within a nanosecond after that,” said Sen. John Kennedy, R-La.

“When you have the votes, you go vote. You don’t wait around for somebody to talk themselves out of it,” he said.

Perhaps the most binding time limit that faced Republicans Tuesday evening was the possibility that they could lose a guaranteed “yes” vote, Sen. Luther Strange of Alabama, for a “no” vote, pending the results of the special Senate election in Alabama.

But Senate Majority Leader Mitch McConnell, R-Ky., discounted that possibility at an afternoon press conference, saying Strange was set to serve until the end of the year before his successor is seated.