New York City Mayor Michael Bloomberg has a promise -- or a threat -- for congressional candidates: In advocating more gun control, he'll put his money where his mouth is.

Just ask the House hopeful who faced over $2.2 million Bloomberg-funded ads -- or talk to the Democrats charged with trying to take back the House majority in 2014.

The billionaire mayor spent the money attacking former Rep. Debbie Halvorson, a Democrat who had been favored to win a Chicago-area House seat, over her "A" rating from the National Rifle Association. On Tuesday, 75 days after 20 children and 6 adults were massacred at Sandy Hook Elementary in Newtown, she lost decisively to former state Rep. Robin Kelly in the Democratic primary for disgraced Rep. Jesse Jackson Jr.'s seat in Illinois' second congressional district.

"This is an important victory for common sense leadership on gun violence, a problem that plagues the whole nation,” Bloomberg said in a Tuesday night statement -- commenting on a special election primary in a district nearly 800 miles from his home. As she conceded, Halvorson blamed Bloomberg's money for her failed campaign.

Her loss is one of the first real data points to dot the political landscape facing President Barack Obama -- and the Democrats he'll need to stand with him -- as he pushes a package of new gun control laws in the wake of the Newtown shootings. The president wants to ban assault weapons like the gun used at Newtown, limit the number of rounds of ammunition in magazines, require universal background checks for gun buyers and make gun trafficking a federal crime.

It would be all but impossible for an assault weapons ban to pass the Senate — and prospects for any new laws are even dimmer in the GOP-controlled House. But lawmakers from both parties say could support requiring anyone who buys a gun to get a criminal background check. Under current law, people who buy guns from private sellers aren't required to get that check.

So why does Halvorson's race matter to the legislative and political fights? After all, skeptics note, gun control isn't a controversial issue in urban Chicago, a city plagued by gun violence and a high murder rate. Bloomberg's tactics would likely be much less effective in a rural swing district with an ingrained hunting culture.

But going after every pro-gun Democrat isn't quite the point, advocates say. Instead, it's a way of reassuring lawmakers -- particularly in swing suburban areas -- that someone will have their back if they support new gun restrictions.

And it's also about telling Republicans in similar situations -- like those who hail from suburban Philadelphia, New York and Denver -- that there's a new threat.

"The NRA has been the only game in town. That's not going to be the way it is anymore, and races like Halvorson's...are intended to send that message," said Mark Glaze, executive director of Mayors Against Illegal Guns, the advocacy group that Bloomberg co-chairs.

In the past, the NRA has aggressively targeted lawmakers who back new gun laws. After a Democratic Congress passed an assault weapons ban in 1994, Republicans swept back to power in the House. The ban was allowed to expire in 2004. This time around, the NRA is opposing universal background checks.

Now, though, Democrats insist Bloomberg's millions amplify a new reality: changing public attitudes in the wake of Newtown. Polls show support for new gun restrictions is higher than it's been in more than a decade. And gun control advocates have retooled their message, focusing on reducing gun violence instead of trying to litigate Second Amendment rights. It's a distinction some Democrats believe will help turn the tide on an issue they've historically struggled with -- one strategist compared it to focusing on raising taxes on the rich during the 2012 campaign, helping their party win on the broader tax issue, where Republicans had previously claimed the upper hand.

There's already evidence that suburban Republicans are staking out support for some new gun laws -- a reality that GOP strategists were eager to point out.

"I think the idea of background checks across the board, I'm not opposed to them," Rep. Joe Heck, R-Nev., told the Las Vegas Review Journal's editorial board. "I disagree with people who say that this is going to be the first step to gun registration, which leads to gun confiscation."

"I agree with the president that we can and should strengthen the nation's background-check system," Rep. Pat Meehan, R-Pa., said in January. Also supporting stronger checks is fellow Philadelphia-area Republican Rep. Mike Fitzpatrick.

After Newtown, polls show support for stricter gun laws is increasing even among Republicans. A new NBC News/Wall Street Journal poll out Tuesday showed 61 percent of Americans think gun laws should be more strict, the highest percentage since 2000, after the Columbine shootings months earlier. That's up from 51 percent in January of 2011, the last time the poll question was asked prior to Newtown. The shift is largely due to Obama's coalition of Democrats, African Americans and Hispanics. But among Republicans, 37 percent now say gun laws should be stricter. Just 24 percent of Republicans said so in January 2011.

Obama and Democrats want to act fast on gun measures to maintain that momentum. In the Senate, Judiciary Committee Chairman Patrick Leahy wants to start the process of writing new gun laws on Thursday. Republicans could push that another week.

In advance of the hearings, Democrats are scrambling to hash out a deal with Sen. Tom Coburn, R-Okla, on a background check bill. Coburn has been negotiating with Democrats for weeks, but talks have stalled in recent days over how to keep track of private gun sales so police can later track guns used in crimes. Democrats and gun control advocates say gun sellers need to keep a record or the law will be toothless, while Republicans argue that could lead to the federal government tracking gun owners.

"There absolutely will not be record keeping on legitimate, law-abiding gun owners in this country," Coburn said on "Fox News Sunday."

The slowed negotiations with Coburn have prompted Democrats, led by West Virginia Sen. Joe Manchin, to ratchet up what's been ongoing outreach to other moderate Republicans who might be willing to sign on. Sen. John McCain said Wednesday that he's been involved in working on legislation.

Leahy's committee is also going to take up the likely doomed assault weapons ban, which California Sen. Dianne Feinstein is sponsoring. Democratic leaders have pledged a floor vote on the measure -- a move Obama urged at his State of the Union address, when supporters in the chamber erupted into chants of, "vote, vote, vote."

Holding the vote is a significant part of the political calculus: It would allow Democrats in red states or swing districts to say they've opposed Obama's plan to ban weapons while still giving them an opportunity to tout support for other measures to reduce gun violence.

"I want it on the floor," Feinstein told NBC News on Tuesday.

NBC's Domenico Montanaro and Carrie Dann contributed to this report.