The apparent goal is to get the legislation scored - a Senate requirement - and hold a vote before the bill or its effects are widely digested by the public.
In an attempt to avoid the heavy backlash and ensure disagreements in the conference don't spill out into plain - as was the case in the House GOP's fight over the American Health Care Act - the Republican Senate majority is crafting the bill largely behind closed doors.
White House spokeswoman Sarah Huckabee Sanders declined to comment, telling reporters aboard Air Force One Tuesday evening, "We don't comment on rumors or private conversations".
Republican senators still disagree on major components of potential legislation, and the meeting with Trump did little to change their minds.
House Republicans have pushed through a bill that seeks to ensure people in the country illegally can not get tax credits to pay their health insurance premiums.
GOP leaders have reportedly been targeting a vote on a health plan before the July 4 recess, but the exact contents of the bill are unclear even to some Senate Republicans. "And he certainly is fine with us taking a different direction with what the House did". House Republicans just passed sweeping bank deregulation.
Trump used those words Tuesday at a closed-door White House lunch with 15 Republican senators, congressional sources say.
Sen. Lamar Alexander, R-Tennessee (r), with Democratic Sen. Lee on the fence, senate leadership are turning to Mr. Cruz.More news: Senate Plan To Replace Obamacare In Trouble
Portman told reporters the group also discussed how to get insurers back in the marketplace quickly. Thus, Trump's suggestions have really complicated things.
The Ohio Republican acknowledged the meeting didn't appear to resolve any differences, but added "that wasn't the objective". "Pretty obviously (he's) not a details guy", said a Republican aide. "I mean it", Trump gushed.
"He talked about making sure we have a bill that protects people with pre-existing conditions and helps people". "From day one, I said we are going to repeal and replace Obamacare".
"Thune said Trump did not lay out policy specifics of what he'd like to see in the bill, nor did he set a deadline for passing legislation through Congress".
Trump will also meet with "Obamacare victims" on Tuesday when he travels to Wisconsin. Call your Senator today to tell them that you do not support the passage of the AHCA, especially if you can't read the bill in its entirety before it is voted on. McCaskill went on to say that she has "no idea of what's being proposed".
Time is of the essence.
Doubts over the future of the bill in the Senate rose after the Congressional Budget Office (CBO) issued a report in May predicting that if the Republican reform is to go ahead, 23 million people in the USA will lose their medical coverage within a decade.