The discussions are still ongoing and a vote isn't likely for several weeks, but several details emerging from the consequential negotiations last week have the party's right flank on edge.

A month ago, there was a lot of optimism that the Senate process would go better for conservatives than the House process initially had. They were given a seat at the negotiating table, with leadership inviting both Sens. Mike Lee of Utah and Ted Cruz of Texas to participate in the Senate's health care "working group." But with leaders seeking to assuage concerns from all sides of the GOP, conservatives are facing potential policy blows.

Republican leaders Tuesday indicated that they preferred not to repeal as many of the Obamacare-era regulations as the House bill did, including a key protection for people with pre-existing conditions that blocks insurers from charging people more for insurance based on their health history.

That could make it tougher for Republican Sens. Lee, Cruz and Kentucky's Rand Paul to vote for the bill after they've warned for months that Obamacare regulations have to go if premiums are going to come down.

Michael Cannon, the director of health policy studies at the libertarian Cato Institute, said from what he can tell, senators are moving little more than "Obamacare with window dressing."

Heritage Action spokesman Dan Holler said of the status of negotiations, "It's a very complex issue, but certainly the way conversations played out publicly this week, there's concern among a lot of conservatives. If you look at Senate conservatives, they are still very involved in the process. That needs to continue."

Also on the table: keeping some of the Obamacare-era taxes in place for at least awhile to reach the $133 billion savings goal that is required under Senate rules.

"That set off alarm bells here," Club for Growth President David McIntosh said Friday. "The Club for Growth would vigorously campaign against that as fake Obamacare repeal. ... If the Senate was trying to send out a trial balloon, consider it shot down."

McIntosh said his group put out calls to Senate offices making it clear they wouldn't support a bill that kept key Obamacare taxes in place. The Club for Growth is working on designing a campaign to promote the Senate's repeal bill right now, but McIntosh warned it will turn the campaign against the bill if they don't feel it's conservative enough.

Also under discussion is a proposed seven-year "glide path" that would phase out Medicaid expansion more slowly than the House bill would and would be a major win for moderates from expansion states.

One conservative GOP aide said they are feeling squeezed out of the process.

"It's is very frustrating because things are happening behind closed door and we are unable to provide input," the aide said. "(House Speaker) Paul Ryan tried that strategy and ended up with a conservative revolt on his hands, we hope next week Senate leadership will shed more light on the details and process."

Leadership can't ignore conservatives. Majority Leader Mitch McConnell can only afford to lose two members and still pass a health care bill. But leadership aides argue that the process is far from a done deal and there are still a lot of details to negotiate. And some conservative members, including Sen. Pat Toomey, a Republican from Pennsylvania, vehemently push back on the idea they're losing steam.

"I'm not convinced it's an accurate characterization at this point," Toomey said.

Republican aides emphasize it's go time. Decisions are going to have to be made soon. Majority Whip John Cornyn told reporters last week that the Senate is likely to vote shortly after the July 4 recess. That would require lawmakers to hammer out the details and then in the next few days give something to the independent Congressional Budget Office to score before the vote.

Republican senators have said they want to wait for the CBO score before their legislation comes to the floor, unlike their House counterparts, who passed their bill last month.

On Tuesday, Republicans will huddle once again at their conference lunch to try and find consensus. Last week's meeting included a menu of options. This week's will give members a more fully fleshed out plan based on feedback. A GOP aide familiar with the negotiations characterized the meeting as likely a red light, green light, yellow light situation.

While outside groups are applying pressure, some conservative members within the GOP conference are slowly coming to terms with the fact that the Obamacare repeal bill may not be as robust as they had once hoped. In the end, they argue, it's about getting a repeal bill passed.

"There are parts we're going to keep no matter what. Twenty-six-year-olds stay on their families' policies, no cap on the amount of coverage you can have. Those are things we're already keeping," said Sen. Tim Scott, a Republican from South Carolina.

Pressed on whether he would be comfortable keeping some of the Obamacare taxes in place, Scott said, "I'm not sure that I'm comfortable. I'm comfortable being a part of 51 senators that improves the outcome of America's health insurance conversation, which requires us to act."

"I think there's gotta be some transition period," said Sen. David Perdue, a Republican from Georgia. "It's gonna take some time to transition out of here."

Sen. James Lankford, an Oklahoma Republican, said his own vision for Obamacare repeal has shifted as the process has gone on.

"It is for everybody because we are dealing with the restrictions of reconciliation rules. All of us are dealing with those clear boundaries," Lankford said. "If you have reconciliation rules and you are dealing with 51 votes, how do you get this done?"

CNN's Ted Barrett and Manu Raju contributed to this report.

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Conservatives say they're losing health care bill fight - CNN