The Senate's push to repeal and replace Obamacare is looking like a game of "I've Got a Secret."

A new report says Senate Republicans are expected to wrap up drafting a bill to reform Obamacare by Monday night.

But Axios.com also reports that GOP leaders don't plan to show that bill to the public — yet.

"We aren't stupid," one of two senior GOP Senate aides told Axios.

"We are still in discussions about what will be in the final product so it is premature to release any draft absent further member conversations and consensus."

Axios noted that Senate Republicans want to vote on the bill before their July 4 recess, and that they expect the bill to be analyzed by the Congressional Budget Office before that planned vote.

CNBC has reached out to the press office for Senate Republicans for comment on the report.

The GOP needs just 50 votes to pass their health-care bill in Senate, given the availability of Vice President Mike Pence to break any tie vote. But Republicans can only afford to lose support for the bill from just two of their 52 senators for that legislation to pass.

The House of Representatives' version of a health-care reform bill, the American Health Care Act, passed the House in May by just a single "yes" vote, which was held before it was analyzed by the CBO. That nonpartisan office later estimated that the AHCA would lead to 23 million more Americans lacking health insurance by 2026 than would be the case if Obamacare remained intact.

The House's bill is broadly unpopular with the general public, multiple surveys have found. The Quinnipiac University Poll released last Thursday found that 62 percent of American voters disapprove of the Republican health-care plan, compared with just 17 percent who approve of it. That is a worsening of support for the plan since May 25, when the same poll found 57 percent of voters disapproved of it, and 20 percent approved.

Republicans, who for years have harshly criticized Democrats for passing Obamacare to law without a single vote in favor of it from a GOP member of Congress, have fast-tracked their own health-care reform bill in a way that is freezing out Democratic participation in its crafting.

The bill is being written by a small group of GOP senators. And Republican leaders in the Senate have no plans to hold hearings on the bill before holding a vote, just as GOP leaders in the House held no hearings on their own version of an Obamacare replacement before passing it.

On Thursday, Sen. Claire McCaskill, D-Mo., lambasted Republican counterparts during a committee hearing where Health and Human Services Department Secretary Tom Price was testifying.

"I heard you, Mr. Secretary, just say, 'We'd love your support,' " McCaskill said. "For what? We don't even know. We have no idea what's being proposed. There's a group of guys in a back room somewhere that are making these decisions. There were no hearings in the House.""

"You couldn't have a more partisan exercise than what you're engaged in right now," she said. "We're not going to have hearings on a bill that impacts one-sixth of our economy."

On Monday, Tom Perez, the chairman of the Democratic National Committee, said, "The American people deserve a transparent legislative process with public hearings and input from experts."

"Behind closed doors, 13 Senate Republicans are crafting a mammoth piece of legislation that could dismantle the entire health care system and deprive 23 million more Americans of access to care, while causing unnecessary spikes in premiums for low-income families, older Americans, and those with pre-existing conditions," Perez said.

"Eight years ago, Democrats passed health care legislation the right way – holding public hearings, meeting with experts, listening to voters, and accepting amendments. With so much at stake, Republicans in Congress owe their constituents the same legislative transparency."