Washington (CNN) If the Senate is about to vote on repealing and replacing Obamacare by the July 4 recess, it would come as a surprise to most in Washington -- especially Republican senators who presumably would be backing the bill.

Earlier this month, Majority Leader Mitch McConnell told President Donald Trump that a vote on health care was possible before Independence Day, but as negotiations continue, members have yet to see bill text and time is running out to get an official Congressional Budget Office score on the bill in time.

"I really don't want to see us vote before the July 4th break. I think it'd be too soon," Wisconsin Sen. Ron Johnson told reporters Thursday.

South Dakota Republican Sen. John Thune, a member of leadership, said he hoped "there's still some magic in the 4th," but admitted "I don't know."

"I think right now we're still batting around ideas, but it's coming together," Thune said.

The July 4 deadline was self-assigned, but not critical to the ultimate fate of the bill. And Republicans have been making substantial progress. GOP leaders have been incrementally sending bits and pieces to the non-partisan Congressional Budget Office for review.

The CBO, which projected the House-passed Obamacare repeal bill could lead to over 20 million people losing health care coverage, won't be able to put together a final report, or "score," in just a few days once -- if -- the Republicans have a final plan. But pre-emptively working with CBO could at least speed things up.

Rep. Mike Enzi, the Senate's Budget Committee Chairman whose committee is taking the lead in writing the health care bill, said "I am pleased with the progress. I don't have a July 4th deadline."

Nothing set in stone

At the end of the day, it's McConnell's call, and he's not letting on.

Rank and file Republicans remain largely in the dark about what will ultimately end up being in their health care bill, making many even more skeptical the legislation is going to be ready and voted on by July 4.

Moderates are holding out hope that they'll see a more gradual "glide path" to end Medicaid expansion and that their leaders will find a way to make the tax credits more generous for low-income people, but nothing is set in stone leaving open a real question of if they'll be able to vote for what comes forward.

"I know the outlines of various proposals that have been discussed, but it is still very much a work in progress," said Sen. Susan Collins, R-Maine.

"There's no bill as far as I know," said Ohio Republican Sen. Rob Portman.

Conservatives unhappy with the plan

Conservatives also don't want the process rushed. They've been arguing to repeal at least as many Obamacare regulations as the House bill did and have been clear that they aren't necessarily comfortable voting on legislation without taking a close look at it.

"[McConnell] gets to choose when he puts something forward, but they have to count the votes and they have to write a bill so it's hard for me to say absolutely yes or no because I haven't seen a bill," said Sen. Rand Paul of Kentucky.

"We continue to have productive discussions. We're not there yet," Texas Republican Sen. Ted Cruz said Thursday. "From the beginning the working group agreed not to set any artificial deadlines but to work until we reached agreement. I think that was the right approach."

Leadership is grappling with a balancing act. Wait too long, and they risk letting their members talk the health care bill to death. Go to soon, and they risk not having enough buy-in to actually pass something. Majority Leader Mitch McConnell can only lose two members. More than that? Game over.

Sen. Roy Blunt, a Republican from Missouri and member of leadership, has he thinks July 4th is a "good deadline," but even he admitted the window might be closing.

"Look, my view is this doesn't get better over time and all of the final work on bringing people together on a bill like that happens in the last 10 days," Blunt said. "You just have to decide which 10 days it is, but there may be just administrative obstacles that I'm not aware of about CBO scoring or getting a bill put together that might push it beyond July 4th."