In a flurry of votes that stretched into the early hours of Thursday, Republicans in the U.S. Senate forced through a budget outline that envisions the repeal of the Obama health law, as GOP lawmakers took the first step of what is expected to be a politically difficult effort to reverse President Obama's signature legislative achievement.

The final vote in the Senate - which wrapped up at 1:25 am - was a narrow 51-49 edge for the GOP.

"The Senate just took an important step toward repealing and replacing Obamacare," said Senate Majority Leader Mitch McConnell (R-KY).

This Senate budget outline contains no details on how to change the system - it just starts the legislative process that would allow Republicans to use the process known as "budget reconciliation" to get a bill through the Senate without the threat of a filibuster.

Only Sen. Rand Paul (R-KY) broke ranks, as he followed through on his promise to vote against the budget outline, worried that it won't rein in spending enough; Paul is also trying to push his fellow Republicans to finalize their plans to replace the Obama health law.

"These ideas have been studied and debated over the years, and it’s time we coalesce around a solution that will work," said Sen. David Perdue (R-GA).

As one might expect, Democrats were not pleased, as they repeatedly voiced their displeasure on the Senate floor as the debate and vote wrapped up.

"Repealing the health care that millions of Americans rely on is cruel and inhumane," said Sen. Chris Murphy (D-CT).

"This is shocking, reckless and immoral," said Sen. Brian Schatz (D-HI).

"They have no plan at all," Schatz added.

The early morning vote in the Senate sends the plan across the U.S. Capitol to the House, where some Republicans have been threatening to vote against the "budget resolution," saying it's time for the GOP leaders to unveil a specific plan to replace Obamacare.

"The quicker we can do it, the better," said Rep. Tom Cole (R-OK), who told reporters that he welcomed any pressure that President-Elect Trump might put on Republicans in the Congress to act.

"I don't have any problem with the President providing a sense of urgency," Cole added.

Some Republicans seemed to welcome that type of intervention, knowing full well that there are difficult decisions that must be made on the details of any health care plan.

"I think we've got an opportunity to follow his lead in this regard, and deliver to the American people the replacement that we've been campaigning on for six years," said Rep. Dennis Ross (R-FL).

"The question is what are the details," said Rep. Mark Meadows (R-NC), who heads the House Freedom Caucus, a group of more conservative members who have been making noise about getting the details in order.

A vote on the budget resolution could come as early as Friday in the House - but GOP leaders may need to twist some arms to ensure that the plan is approved.