By Kristina Peterson and Natalie Andrews

WASHINGTON--The Republican-controlled Senate narrowly passed a budget resolution early Thursday morning, clearing the first major hurdle in the GOP effort to repeal the Affordable Care Act.

After spending years criticizing the 2010 health law, Republicans have made eliminating it their priority since the new session of Congress began last week. But they have yet to coalesce around a plan to replace the law, casting some doubt over how the process would unfold over the next few weeks. Many Republicans are uneasy over voting to repeal the law without knowing what would take its place.

"The Senate just took an important step toward repealing and replacing Obamacare by passing the resolution that provides the legislative tools necessary to actually repeal this failed law while we move ahead with smarter health-care policies," Senate Majority Leader Mitch McConnell (R., Kentucky) said in a statement after the resolution passed.

President-elect Donald Trump has sent mixed messages to Republicans about how to approach the health law's dismantling.

In a Twitter message last week, he warned Republicans to be careful about assuming political responsibility for dismantling the law. In a press conference Wednesday, Mr. Trump said that, once his secretary of the Department of Health and Human Services is in office, he would put forward a plan to "almost simultaneously" repeal and replace the health law.

House and Senate Republicans said that, meanwhile, they would continue the complicated procedural maneuvering that could enable them to repeal large sections of the health law.

Thebudget for fiscal year 2017, which squeaked through the Senate in a 51-48 vote, sets up the next step by instructing two House and two Senate committees to come up with plans for wiping out much of the health law.

Those proposals would then be combined into legislation which, because it is tied to the budget, could clear the Senate with only a simple majority. Most bills need 60 votes to clear the Senate, where Republicans hold 52 seats.

Sen. Rand Paul of Kentucky was the only Republican to join all of the members of the Senate Democratic caucus in opposing the budget. Senators stifled yawns and debated until just after one in the morning, with both Republican and Democratic lawmakers trying to add amendments to the resolution before it was brought to a vote. No amendments passed.

Mr. Paul opposed the budget over its spending levels, which he believes add too much to the federal budget deficit.

To show their opposition to the resolution, Democrats voted one by one from their desks on the Senate floor. Each senator stood up and called out their "no" vote, though most of the Republican lawmakers had left, and debate isn't allowed during a vote.

The budget's spending levels are in line with those agreed to in a two-year budget deal reached by Congress and the Obama White House in the fall of 2015. Changing them could complicate efforts to fund the government for the final five months of the fiscal year. The government's current funding expires at the end of April. Most Republicans have said they would focus on cutting spending when they write a budget this spring for the coming fiscal year 2018.

Senate Democrats have been unified in opposing Republican efforts to repeal the health-care law, which has expanded coverage for roughly 20 million people. A large number are lower-income people who have been covered through Medicaid expansions in 31 states andthe District of Columbia.

"Millions of women, who were pregnant or survived diseases like cancer, are able to keep seeing their doctors without fear of their health insurance being taken away by the insurance companies," Sen. Kirsten Gillibrand (D., N.Y.) said on the Senate floor Wednesday.

Republicans say the law has hurt the economy by requiring companies to spend more on health care and has imposed crippling requirements and taxes that have driven up health-care costs. They say the law is faltering amid premium increases in 2017 on the exchanges where consumer can buy policies, decisions by some insurers to leave the exchanges and lower-than-expected enrollment.

The House is expected to vote Friday on the budget resolution in what is likely to be a largely party-line vote. However, some Republicans said they want more information about the GOP plan to repeal the health law before the vote on the budget measure.

"It isa vehicle. Then the question is, 'What's in the vehicle?'" Rep. Dave Brat (R., Va.) told reporters Wednesday. Mr. Brat said he was hoping to get enough information to be able to support the budget Friday. "We all want to vote yes."

Write to Kristina Peterson at kristina.peterson@wsj.com and Natalie Andrews at Natalie.Andrews@wsj.com

(END) Dow Jones Newswires

January 12, 2017 02:19 ET (07:19 GMT)

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