Three Democratic Senate aides with knowledge of where members stood on the nomination said Friday that enough Democrats could oppose Dr. Murthy that he would most likely fail to be confirmed if a vote were held soon.

Senator Mark Begich of Alaska, who is up for re-election, has said that he will probably vote no. Mr. Begich, who has received angry letters from Alaskans who say they are alarmed by what they believe are Dr. Murthy’s antigun views, wrote to his constituents recently: “I will very likely vote ‘no’ on his nomination if it comes to the floor. I share your concern about Dr. Murthy’s views in favor of gun control.”

Coming nearly a year after a gun-control bill drawn up after the massacre at Sandy Hook Elementary School in Connecticut went down in defeat in the Senate, the N.R.A.’s highly aggressive and visible campaign against Dr. Murthy shows how the organization has determined that its greatest chances for success in Congress come when it holds nothing back.

The group has already begun gearing up to be a strong presence in congressional and governor’s races. Since late last year, it has hired dozens of field strategists to begin laying the groundwork for campaigns in politically competitive states.

Though Dr. Murthy has expressed a desire to see more restrictions on how guns can be purchased and who can own them — views in step with where many Americans stand on gun control — the N.R.A. has dismissed him as a radical.

In a letter to senators last month, Chris W. Cox, the group’s chief political strategist, mentions Dr. Murthy’s support for limits on ammunition purchases, a ban on “popular semiautomatic firearms” and the removal of restrictions that keep the Centers for Disease Control and Prevention from funding “antigun advocacy research.” Mr. Cox also cited Dr. Murthy’s calls for a federal gun buyback program for assault weapons and for mandatory safety training for gun owners. Dr. Murthy has said his concerns about guns stem from his experience in the emergency room where he has witnessed the trauma that gun violence can cause.

The surgeon general’s office — which deals with policies of medicine and public health — is not usually a focus of gun-rights advocates. But an N.R.A. spokesman, Andrew Arulanandam, said that it was taking no chances that under Dr. Murthy the office would veer into gun policy. “All the rules have changed as far as this White House is concerned,” he said. “Given Dr. Murthy’s blatant activism on behalf of gun control, that’s not a gamble we’re willing to take.”