Last week, New York City Mayor Mike Bloomberg sent a letter to hundreds of the biggest Democratic donors in New York, urging them to refrain from giving money to the four Democratic senators who voted against a bill that would have expanded background checks on gun purchases.

But interviews with a number of these top Democratic givers reveal that like some other Bloombergian initiatives—soda bans, bikes shares, and breast-feeding mandates, to name a few—this directive is being met with some skepticism.

“His heart is in the right place, and I have respect for his values, but his political judgments are just wrong,” said Victor Kovner, who, along with his wife, Sarah, has been a regular contributor to Democratic causes for decades. “He has little experience in politics. He has experience running the city and running as a billionaire for office, and running the city well, but by reason of his limited political background, he has been mostly focused on the merits [of the gun legislation] and not on the politics.”

The gun control bill, named after West Virginia Democrat Joe Manchin and Pennsylvania Republican Pat Toomey, would have required that all gun purchases be subject to a background check. (Current law exempts guns sold by private dealers and at gun shows.) Bloomberg has been a longtime proponent of stricter gun laws, founding Mayors for Illegal Guns in 2006, but the mass shooting at an elementary school in Newtown, Connecticut, late last year precipitated a furious lobbying push by him and other gun control advocates.

In the end, it was not enough. Four Democrats—Mark Begich of Alaska, Mark Pryor of Arkansas, Max Baucus of Montana, and Heidi Heitkamp of North Dakota—joined all but four Republicans to ensure the bill’s defeat. All four of the Democrats hail from swing states and are expected to face tough reelection fights that would be crucial for Democrats to win if they hope to hold on to their slender majority in the Senate. Both Begich and Pryor are up for reelection in 2014; Heitkamp isn’t up until in 2018. After the vote, Baucus announced his retirement.

Most political analysts put the odds of a GOP takeover of the Senate at about even. A number of donors who spoke to The Daily Beast expressed disappointment in the vote of the four senators, but thought the chances of getting even the most modest kind of gun legislation passed would be brought to zero if Mitch McConnell led a GOP majority in the Senate after November.

“It took me a long time to figure this out, but it actually matters a lot which party has more members in the Senate,” said Sally Minard, one of the top Democratic fundraisers in New York. “It is just critical that Democrats take back the House and control the Senate.”

Bloomberg’s efforts are not entirely alone. Kenneth Lerer, chairman of BuzzFeed, and David Bohnett, a technology entrepreneur in Los Angeles, have both said they are withholding contributions to Democrats who aren’t right on the issue. And former White House chief of staff Bill Daley wrote a Washington Post op-ed urging his fellow Democrats not to give to Heitkamp and the others.

But it is one thing to hear from Bill Daley, who hails from one of the most prominent Democratic families in the country, and another to hear from Mike Bloomberg on the matter. New York’s top Democratic donors are some of the city’s titans in real estate, finance, and law, exactly the kind of community that the billionaire media mogul turned mayor moves easily in. But some bristled at suggestions on political giving put forth by an independent who was three times elected mayor of New York as a Republican and who has regularly donated to Republicans around the country, including to some with shaky records on gun control.

“As much as you are not happy with the way [the four] voted, do we really want to jeopardize the Senate majority in states where it is already jeopardized?” asked one top New York donor, who requested anonymity to avoid antagonizing the mayor. “God forbid we lose this.”

It was a letter, some noted, that could have easily been endorsed by the likes of Karl Rove and other Republican operatives who would like nothing more than to see marginal Democrats starved of campaign funds.

“If the mayor didn’t send his letter to Republicans also,” said Kovner. “Then it wasn’t worth the paper it was printed on.”

Gun control advocates have long strategized around ways to defeat the immense power of the National Rifle Association, which has used a scorecard and a checkbook to keep lawmakers in line. Other gun control groups, however, have traditionally preferred a far less confrontational approach than Bloomberg is taking, and top Democratic officials noted that none have officially lined up behind his letter.

Ladd Everitt, the director of communications for the Coalition to Stop Gun Violence, said that his group largely supported what the mayor was doing, and that they did not endorse the letter because “we were not asked to.”

“If the NRA has chips in the game, we want to have chips in the game too, and a way to pressure people who are not voting on principle is to deny them chips,” he said. “We have reached the point where we have these insane gun laws precisely because we have been too afraid to go after our ‘friends.’ If we had taken a harder line on this maybe we wouldn’t be in this situation.”

And a number of Democratic donors who spoke to The Daily Beast said they supported what the mayor was doing.

“It is not about advocating for their defeat. But if a public official is going to cast a vote that is going to endanger the welfare and the lives of New Yorkers and citizens throughout this country, we are going to hold them accountable,” said Robert Zimmerman, a major Democratic donor in New York. “Look at Chuck Schumer. He has been a role model and a hero when it comes to gun safety, and we have a right to elect senators of a similar caliber.”

It remains unclear how much of an effect all of this campaign-fund withholding will have in the end. Heitkamp doesn’t face the voters for five and half more years. Begich recently had a New York fundraiser canceled, but the host insisted it was due to scheduling and not to the mayor’s letter. Last month, Bill Clinton hosted a fundraiser for Pryor.

“Our fundraising has been pretty good. I haven’t seen any change in any of that at all,” said Jeff Weaver, his campaign manager. “We haven’t had donors turn us down because of what the mayor wrote. We are continuing to fundraise as we always have.”

Instead of withholding funds and encouraging others to do the same, top Democratic donors suggested that there were other ways to change the conversation around gun control. Some suggested that the money would be better spent rewarding those Democrats and Republicans who took tough votes in favor of the measure. Or defeating some of the vulnerable Republicans in the House who do not support gun control. If the House flipped back to Democratic control because of the gun issue, this thinking goes, it would send a message to GOPers around the country. And others noted that the four took votes that they thought would reward them politically in their home states; instead of punishing them, better to educate voters in each of those states around the dangers of gun violence.

“It would be wonderful if we were able to give Democrats who were afraid to vote for it some kind of cover,” said Minard. She said advocates needed to do more old-fashioned arm-twisting in order to get their way.

“I mean, we have all seen the movie Lincoln, haven’t we?”