WASHINGTON (CBSNewYork/AP) — The Republican-controlled Senate has taken one of the first steps toward dismantling President Barack Obama’s health care law.

In a nearly partly-line vote of 51-48, lawmakers approved a nonbinding GOP-backed budget measure that makes it easier for action on subsequent repeal legislation as soon as next month.

Republicans have been promising to get rid of “Obamacare,” but more and more of the GOP are feeling uneasy about dumping it without having a replacement in place.

“We must act quickly to bring relief to the American people,” said Senate Majority Leader Mitch McConnell, R-Ky.

The House plans to vote on the measure Friday.

At a news conference Wednesday, President-elect Donald Trump said a replacement will be offered with the confirmation of his health secretary.

“We are going to have a healthcare that is far less expensive and far better,Trump said.

Trump has repeatedly said that repealing and replacing “Obamacare” was a top priority, but he has never fully explained how he planned to do it.

Conn. Sen. Richard Blumenthal is among Democratic lawmakers saying this is too dangerous a path, WCBS 880’s Fran Schneidau reported.

“The effects of this repeal will be almost immediate because insurance companies will begin abandoning the markets,” he said.

Blumenthal says Democratic lawmakers want to stop this train before there’s a wreck, thus putting an end to health care coverage for the millions of people who rely on the plan.

(TM and © Copyright 2017 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2017 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)