What's next in the Republican health care push

McConnell said the Senate will hold a procedural vote "early next week."

When that happens, 50 GOP senators must vote yes in order to open up debate on a health care plan that the U.S. House of Representatives passed in May of this year. Then, the repeal-only language that was initially passed and subsequently vetoed in 2015 would be added to the bill as an amendment. The Senate's repeal-only plan would allow for a "stable two-year transition period."

But there are some ardent supporters who have come out in favor of repealing even though they were publicly opposed to the replacement plan.

"I still favor a replacement," he added. "But what we discovered is Republicans don't agree on a replacement."

Earlier this week, Paul urged his fellow lawmakers to consider their constituents.

“If you're not willing to vote the same way you voted in 2015, then you need to go back home and explain to Republicans why you're no longer for repealing Obamacare,” Paul said.

"My hope is that means there are full legislative hearings, that we have determined what can be done to improve access to affordable healthcare across the country. In a sound, fiscal kind of way," Moran told reporters.

Other actions being taken

One lawmaker is taking actions to try and quell any confusion about what happens during the turbulent discussions.

“However the votes come out on the health care bill, the Senate health committee has a responsibility during the next few weeks to hold hearings to continue exploring how to stabilize the individual market. I will consult with Senate leadership and then I will set those hearings after the Senate votes on the health care bill,” Alexander said in a statement.

Trump’s plan moving forward

Trump said Tuesday that he was “very disappointed” in the Senate’s failure to get a health care bill passed.

Trump also said he doesn't think the Republican plan "is dead" but it "may not be as quick as we had hoped but it is going to happen."

The White House invited all 52 Republicans over for lunch today in an effort to help the party come together on the health care issue.

"I will be having lunch at the White House today with Republican Senators concerning healthcare. They MUST keep their promise to America!" he wrote.

"The Republicans never discuss how good their healthcare bill is, & it will get even better at lunchtime.The Dems scream death as OCare dies!" the second tweet reads.

Ali Rogin contributed to this report.