WASHINGTON ― Within minutes of the House passing a bill to repeal the Affordable Care Act, Sen. Lamar Alexander (R-Tenn.) took to the Senate floor to congratulate the other body, and pronounce the legislation all but dead.

“The Senate will carefully review the House bill, and now we’ll go to work on a Senate bill,” said Alexander, who chairs the Health, Education, Labor and Pensions Committee that will play a key role.

“There is an urgency, but we want to get it right,” Alexander said, emphasizing the “get it right” part repeatedly.

Republicans in the House managed to barely pass their American Health Care Act Thursday, just before taking a week off, but it required numerous fits and starts and an all-out lobbying effort by House leaders and the White House. In the end, they did so without holding any hearings on the measure or getting cost estimates from Congress’ nonpartisan Congressional Budget Office.

“There’ll be no artificial deadlines” in the Senate, Alexander said. “We will make sure we know what our bill costs when we vote on it.”

Unlike in the increasingly fractious House, senators are better at talking to one another, and Alexander said after leaving the floor that he thought GOP senators very much wanted to come up with their own plan. But he he stopped short of predicting success.

“The mood, at least in the Republican caucus, is we’d like to get to yes if we can. Now we have many different opinions, and no one doubts this is difficult,” Alexander said.

He was even less willing to say whether Republicans in the Senate could agree with colleagues in the House on a compromise version, should the Senate pass something.

“Oh, I’m not going to try to predict that,” Alexander said.

Gary Cameron / Reuters

The difficulty in the Senate is that a number of Republicans are intent on preserving the Obamacare expansion of Medicaid in their states, and determined to keep Obamacare protections for people with pre-existing medical conditions.

The House plan would cut Medicaid spending by at least $800 billion, and give much of that money to wealthy taxpayers. It also leaves the issue of pre-existing conditions up to states, which could waive Obamacare requirements.

How to satisfy House conservatives, who insisted on the Medicaid cuts and the waiving of pre-existing condition rules, while also satisfying senators who want to protect those items may not be possible.

Sen. Orrin Hatch (R-Utah), who chairs another committee key to the process ― the Senate Finance Committee ― expressed optimism that it could be done, even as he acknowledged the difficulty.

“It’s close to near-impossible,” Hatch said when asked about it by HuffPost. “I’ve been to near-impossible a number of times, and we’ve always got it done.”

Republicans are trying to pass their repeal through a budget process called reconciliation, which allows measures dealing with revenue and spending to pass the Senate with a simple 51-vote majority, and no threat of a filibuster.

Still, any measure can only afford to lose two of the 52 Republicans in the chamber and still pass. At least a half-dozen GOP senators have already expressed opposition to the tack the House was taking.

One of them, Sen. Susan Collins (R-Maine), said as she was leaving Thursday that she still had grave concerns about the legislation the House passed.

Asked if the Senate could even achieve its own bill, Collins didn’t sound especially confident.

“Boy, that’s a good question. I truly don’t know,” Collins said.

One reason the Senate has to pass its own measure is the Byrd Rule, an obscure procedural edict named after the late Sen. Robert Byrd. It says policy issues that do not affect spending and revenue cannot be passed with the reconciliation process. It would be up to the Senate parliamentarian to decide if everything in the House bill fits within that rubric, but Democrats have argued repeatedly that there is no way the measure would pass the test.

That would mean that any repeal bill would need 60 votes, including eight Democrats ― who have been united in opposition.

Assuming the Senate can pass a bill, the House would have to pass the same measure in order for it to become law. But that seems unlikely, considering the conflicting objections on both sides of the Hill.

More likely, both chambers would send their conflicting legislation to a conference committee in hopes of finding a compromise. But again, the resulting deal would still have to pass muster with conservatives in the House, who already killed an earlier repeal bill that was less extreme than what passed. And those six senators already opposed the less-extreme version.