Several Senate Republicans spent the weekend highlighting their objections to a sweeping draft health care bill and the rapid pace at which it’s moving in the chamber, even as GOP leaders would like to pass the measure before the July Fourth recess.

“I would like to delay this thing. There’s no way we should be voting on this next week,” Sen. Ron Johnson, R-Wis., said on NBC’s “Meet the Press” on Sunday. “No way.”

Johnson said there won’t be enough time for his Wisconsin constituents to digest the bill and give him their feedback under the current schedule. He suggested he might not be able to vote for a procedural motion on the bill, but didn’t go as far as completely ruling out his support.

“Let’s not rush this process,” he said.

Dean Heller, R-Nev., already said Friday he was not inclined to vote for the motion to proceed to the bill, which could occur as soon as Tuesday.

Senate Majority Leader Mitch McConnell of Kentucky faces a daunting legislative task in keeping his conference tightly unified on the health care bill, which would undo parts of Democrats’ 2010 health law (PL 111-148, PL 111-152). Republicans intend to clear the measure under special budget rules known as reconciliation. This approach allows legislation to move on simple majority votes.

With Vice President Mike Pence available to break a tie, McConnell can afford to have two of the Senate’s 52 Republicans reject the health bill. The measure is largely based on the House-passed bill (HR 1682), but with deeper future reductions envisioned for the growth in Medicaid spending.

The Congressional Budget Office will weigh in as early as Monday on how much the Senate bill will save and how it will affect Americans’ medical coverage. CBO said the House bill that passed last month could result in 23 million people losing coverage through reduced growth in Medicaid spending and changes to private insurance subsidies and rules. Sen. Susan Collins, R-Maine, said on ABC’s “This Week” that she has “serious concerns” about the potential for loss of coverage, particularly for rural hospitals and nursing homes. Medicaid is a major funder of care in these settings.

Collins also said she will fight to strip from the Senate bill a provision to block federal funds for the women’s health organization Planned Parenthood. She said she expects to win on the issue, as Democrats likely would back her bid to preserve funding for Planned Parenthood. A victory for Collins on this matter, though, will make the bill less palatable for conservatives.

“It’s hard for me to see the bill passing this week. But that’s up to the majority leader,” Collins said. “We could well be in all night a couple of nights working through what will be an open amendment process. ”

On the same program, though, Sen. Rand Paul, R-Ky., indicated a potential path forward for McConnell. Last week, Paul joined Johnson and two other conservatives in openly criticizing the Senate health bill and saying that its current form fell short of their demands.

Yet conservatives like Paul may find themselves reluctantly voting for the measure: He said he’s made it clear to GOP leaders that he may be willing to compromise to score a partial win in repealing parts of the 2010 health law.

“If they get to impasse, I’ve been telling leadership for months now, I’ll vote for a repeal. And it doesn’t have to be 100 percent repeal,” Paul said. “If you offer me 90 percent repeal, I’d probably would vote it. I might vote for 80 percent repeal.”