WASHINGTON — Senate Republicans took their first major step toward repealing the Affordable Care Act on Thursday, approving a budget blueprint that would allow them to gut the health care law without the threat of a Democratic filibuster.

The vote was 51 to 48. During the roll call, Democrats staged a highly unusual protest on the Senate floor to express their dismay and anger at the prospect that millions of Americans could lose health insurance coverage.

One by one, Democrats rose to voice their objections. Senator Maria Cantwell of Washington said that Republicans were “stealing health care from Americans.” Senator Ron Wyden of Oregon said he was voting no “because health care should not just be for the healthy and wealthy.”

The presiding officer, Senator Cory Gardner, Republican of Colorado, repeatedly banged his gavel and said the Democrats were out of order because “debate is not allowed during a vote.”