Sen. John McCain, (R-Ariz.), was quoted Tuesday in a Bloomberg story saying "no" when asked if he had seen the bill.
"Nor have I met any American that has," McCain reportedly said. "I'm sure the Russians have been able to hack in and gotten most of it."
Sen. Mike Lee, R-Utah, during a Facebook video stream, said, "I haven't seen it yet either, even though I've been a a member of this working group of Senate Republicans" originally put together to work on the bill.
"It isn't being written by us," Lee said. "It's apparently being written by a small group of staffers in the Senate leadership."
"I share your frustrations," Lee said in his message to constituents. "I share it wholeheartedly."
That unusal secrecy and plans for no committee hearings have angered Democrats and raised concerns that a quick vote on the bill will prevent enough opposition to it from being mounted among the public to prevent its passage.
On Tuesday, a trio of Democratic lawmakers traveled to to the CBO's offices in a futile, Facebook-live-streamed effort to see the draft of the bill.
A House version of the bill, which passed by just one yes vote, was projected by the CBO to lead to 23 million more uninsured people by 2026.
"I wouldn't want to compare it to the House bill," McConnell said Tuesday. "It will speak for itself."
The House bill is broadly unpopular with the public, multiple polls have shown.
At the White House, press secretary Sean Spicer said, "I don't know that," when asked if Trump had seen a draft of the Senate's bill.
"I know the president has been on the phone extensively with the leader [McConnell] and key senators," Spicer said. "I don't know that he's seen the legislation or not, but they've been working extremely hard and the president has been giving his input and his ideas and feedback."
"And he's very excited about where this thing is headed," Spicer said.
Spicer said he also didn't know if White House staff has seen the bill, but added that staff is working closely with the senate on the issue.
"I don't know where we are in terms of final plans," he said.
Spicer also was asked about a CNBC report that Trump had told major tech executives on Monday that the Senate bill "needs more heart."
The press secretary said, "The president clearly wants a bill that heart in it."
The Senate needs just 50 votes to pass the bill, assuming a tie would be broken by Vice President Mike Pence. The GOP has just 52 senators, which means the party can afford to lose just two votes among its caucus, because all Democrats and independent senators are expected to vote against the bill.
The bill is expected to significantly reform the way the federal government provides financial assistance to help people pay for individual health plans, and how the government funds Medicaid, the health coverage program for the poor.