Mr. Bloomberg’s strategy creates a tricky situation for Senate Democrats. They do not wish to alienate the billionaire mayor, who has become increasingly aggressive and outspoken on the issue. But they say he should be more sympathetic, given that their party, with its fragile majority, has tried to take on the difficult subject of increasing restrictions on guns in the face of hostility from Republicans.

“What they are doing,” said one senior Democratic aide who, like many people interviewed for this article, declined to go on the record criticizing the mayor, “is increasing the likelihood of a 100 percent A-rated N.R.A. Republican being elected.”

For Senator Charles E. Schumer, the New York Democrat who was an architect of his party’s takeover of the Senate in 2006 and has aggressively built up the Democratic donor base in New York, and who is a close ally of the mayor, the notion that Mr. Bloomberg’s efforts could cost Democrats their majority is not an abstraction.

He praised the mayor’s effort, but added, “We should be mindful that pro-gun safety laws have a much better chance of passing under a Democratic Senate majority than a Republican one.”