Meanwhile, Sen. Ron Johnson, R-Wis., sought to further reduce the tax burden on pass-through businesses, which pay individual rates.
Johnson told reporters Monday that he was working to strike a deal with Senate leaders to bring the benefits for those businesses more in line with the cuts planned for large corporations, which would see their income tax rate fall from 35 percent to 20 percent. According to the report, that's because the Senate Republican tax plan would eliminate the Affordable Care Act's individual mandate - a move the CBO says would raise premiums by 10% a year and cause the poor to be unable to afford insurance.
On Twitter just hours before the scheduled meeting at the White House, Trump also accused Senate Minority Leader Charles Schumer of NY and House Minority Leader Nancy Pelosi of California of being soft on crime, taxes and illegal immigration.
That invitation was swiftly rejected by Senate Majority Leader Mitch McConnell of Kentucky and House Speaker Paul Ryan of Wisconsin.
While these changes appear to address the concerns of a slew of GOP members, a slew of questions remain: Will these changes be adopted by leadership?
The group discussed a slew of changes to the bill, including a "fiscal trigger", adjustments to the state and local tax deduction repeal, and a follow-up bill for Obamacare. If more than two members vote against the bill on the Senate floor, it will fail.
It is not strictly necessary to pass the tax bill through the Senate Budget Committee, where Republicans are hoping to combine the tax bill with a provision allowing for oil and gas drilling in the Arctic National Wildlife Refuge. Will they abide by Senate rules?More news: Missing child alert issued for Neptune Beach teen
"We're in very good position", he said.
If the Senate approves its tax measure later this week, it would need to be reconciled with a version already approved by the House of Representatives before anything could be sent to the White House for Trump to sign into law.
While the overall architecture of the two bills is similar, there are significant differences.
Spokespeople for the Senate Finance Committee, which drafted the bill, did not immediately respond to a request for comment.
"We're looking forward to finding common ground in conference, finalizing the details, and sending this historic legislation to the President by the end of the year", Brady said in remarks to the American Enterprise Institute. Republicans maintain that gap would be narrowed by additional economic growth.
Other Republicans, however, are taking a less lofty view of the legislation. "We got a commitment that puts us in a pretty good place", he said.