Sen. Mike Lee, R-Utah, on Tuesday, lamented the process by which Republicans in the Senate are working to write a healthcare bill, saying he had not read a version and that members were needlessly rushing toward a vote.

"If you're frustrated by the lack of transparency in this process, I share your frustration. I share it wholeheartedly," Lee said, speaking in a video he posted on his Facebook page after noting his office had received a lot of calls. "The American people need and deserve to see legislation as it moves through the Senate."

"We should have been able to see it weeks ago if we are going to be voting on it next week," he added.

Lee, a conservative member of the party, said that he had understood that as being part of the healthcare working group he would contribute to writing the bill, but said he hadn't seen it and that "as far as I know the overwhelming majority of my colleagues haven't been able to see it either."

"It has become increasingly apparent in the last few days that even though we thought we were going to be in charge of writing a bill within this working group, it's not being written by us, it's apparently being written by a handful of staffers who are members of the Republican leadership in the Senate," he said.

Senate Majority Leader Mitch McConnell, R-Ky., confirmed Tuesday that a healthcare bill's text would be released Thursday, with a Congressional Budget Office score and vote expected next week ahead of the July 4 recess. Democrats have blasted Republicans for the speed at which they are moving and for holding healthcare meetings behind closed doors. It's unclear what specifically will be included in the Senate version of the bill, but the House version, the American Health Care Act, threatens to raise number of uninsured by 23 million over a decade and repeals Obamacare's individual mandate, Medicaid expansion and its taxes, and would allow tax credits to help people buy private insurance.

Some reports have signaled that the Senate bill is moving left, prompting House conservatives on Monday to send a letter to Senate leaders encouraging them to keep certain priorities in place, including blocking family planning funding, which covers testing, cancer screenings and birth control, from going toward facilities that also provide abortions.

Lee did not signal how he would vote, but he openly asked during his video why the Senate should be moving forward on the legislation given that it hadn't been made public and that not even senators had seen it.

Republicans are using a budget measure known as reconciliation to advance their healthcare legislation, a move that requires only a simple majority rather than the 60 required to overcome a filibuster. Because they have only a narrow majority, however, they cannot lose more than two votes in the Senate to guarantee passage, assuming a tie-breaking vote by Vice President Mike Pence.

"There is no question that people need relief from Obamacare," Lee said. "There is no question that healthcare has become unaffordable in recent years. The big question is what we are going to do about it and why we have to act so quickly that we necessarily have to be voting on it next week. I'd be fine, don't get me wrong, to be voting on something soon, but we should be able to see it first.