Senate Majority Leader Mitch McConnell of Ky. walks into the Senate Chamber at the Capitol. (Andrew Harnik/AP)

The Senate returns to Washington on Monday with its GOP leaders determined to vote this week on their years-long quest to demolish the Affordable Care Act, even though the goal remains mired in political and substantive uncertainties.

Central questions include whether enough Senate Republicans will converge on any version of their leaders’ health-care plan and whether significant aspects of the legislation being considered can fit within arcane parliamentary rules.

Sen. John Barrasso (R-Wyo.) indicated on Sunday that the majority party may not have enough support to prevail on even a first step — a routine vote to begin the floor debate.

“We’re continuing to work with all of the members. We’re getting much closer to that,” Barrasso, one of the chamber’s few physicians, said on CBS’s “Face the Nation.”

Meanwhile, the two Republicans who have been the effort’s most outspoken foes in the Senate relaunched complaints that their leaders are leaving them clueless as to what exactly will be put forward.

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Late last week, Majority Leader Mitch McConnell (R-Ky.) adopted a strategy uncharacteristic for a tactician who usually spares his caucus needless difficult votes.

Several days earlier, McConnell had lacked enough support to call for a vote on a bill that would rescind parts of the ACA and replace them with a variety of conservative health policies. He quickly switched, saying the chamber would vote anew on a repeal-only measure passed in late 2015 by both the Senate and House — and vetoed by then-President Barack Obama. Less than 24 hours later, that idea faltered, too.

So McConnell has resorted to a plan C: bringing to the floor an anti-ACA bill passed by the House this spring and allowing senators a sort of free-for-all for substituting in either of the Senate measures or new iterations.

“We are still on track . . . to have a vote early this week,” a McConnell spokesman said on Sunday. “The Senate will consider all types of proposals, Republican and Democrat.”

But Sen. Susan Collins (R-Maine), a centrist who says the Senate’s Better Care Reconciliation Act would cut Medicaid in ways that would hurt rural and vulnerable Americans, derided that strategy during an appearance on “Face the Nation.”

Lawmakers “don’t know whether we’re going to be voting on the House bill, the first version of the Senate bill, the second version of the Senate bill, a new version of the Senate bill or a 2015 bill that would have repealed the Affordable Care Act now and then said that somehow we’ll figure out a replacement over the next two years,” Collins said.

“I don’t think that’s a good approach to facing legislation that affects millions of people and one-sixth of our economy,” she added.

Her sentiment was echoed by conservative Sen. Rand Paul (R-Ky.), who contends that the main GOP proposal the Senate has been considering does not go far enough to undermine the ACA. “The real question is, what are we moving to? What are we opening debate to?” Paul said on CNN’s “State of the Union.” He reiterated that he only would support a bill that would remove large portions of the ACA — and not legislation continuing federal subsidies that help millions of people afford their insurance premiums.

Such ideological crosscurrents within his own party are what McConnell has been trying to surmount. The GOP has a narrow majority of 52 senators, and Democrats are unified against the effort to dismantle Obamacare. Given this partisan terrain, Senate leaders are relying on a legislative process known as reconciliation, which allows a bill to be passed with a simple majority when it has budget implications, rather than the customary 60 votes needed to ward off a potential filibuster by opponents.

But the reconciliation strategy hit a roadblock late Friday as Senate Democrats released a set of guidance from the chamber’s parliamentarian, who concluded that aspects of a June 26 version of the Better Care Reconciliation Act probably would not fit within the budget rules. The guidance says several parts of the proposal would require a full 60 votes for approval, including limits on funding for Planned Parenthood and health plans that provide coverage for abortion — both restrictions conservatives have favored.

The parliamentarian also cautioned against a significant part of the GOP bill meant to encourage Americans to maintain health coverage: allowing health plans to freeze out for six months applicants who have allowed their coverage to lapse.

McConnell’s spokesman, Don Stewart, noted that the parliamentarian similarly cautioned against portions of the 2015 ACA repeal bill, but it still passed through the reconciliation process. Neither Stewart nor other Senate staffers said what changes could be contemplated to get around the parliamentary problem.