During a speech in Denver to amp support for gun-control legislation, President Obama renewed pressure on Congress to enact stricter background checks. (Nicki Demarco/The Washington Post)

Sen Mark Begich declared a “sea change” in the politics of gun control immediately after the school shooting in Newtown, Conn., telling his local newspaper that he would not hesitate to buck the powerful National Rifle Association.

But in the months since, the gun rights group has made itself impossible for the Alaska Democrat, and many other lawmakers, to resist.

Begich has signed on as a co-sponsor of a bill, drafted in consultation with the NRA, that would change the way mental illness is reported in the background check system — a measure that critics say could make firearms more easily available to the mentally ill.

Over the past two weeks, while Congress has been in recess, Begich said he was approached repeatedly by constituents who echoed NRA views, telling him not to, in his words, “mess with our gun rights” or “ban anything.”

The NRA’s recent successes on Capitol Hill — as well as a string of victories in state legislatures across the country — demonstrate the effectiveness of the group’s strategy to overcome a post-Newtown tilt toward gun control. The organization has drafted and circulated legislation, mobilized its members and continued to put pressure on politically vulnerable lawmakers. At the same time, groups attempting to promote stricter gun- control measures have faltered.

How the NRA exerts influence over Congress

New restrictions that a couple of months ago seemed possible, even likely, such as bans on assault weapons and universal background checks on gun purchases, are now in doubt.

“The NRA is one of the most important groups in my state,” said Begich, one of several Democrats from conservative states who are up for reelection next year. He and others like him are the swing voters in the gun debate in the Senate, where deliberation over new legislation is expected to begin this month.

The gun rights group has suffered some serious setbacks since the December school shooting. New gun limits have passed in reliably liberal Maryland and New York and in Colorado and Connecticut, where two of the most recent shooting rampages occurred.

But even gun-control advocates acknowledge that the NRA is getting the better of them, both in Congress and state capitals across the country.

The NRA’s congressional operation is so effective that one of the gun lobby’s most outspoken critics, Sen. Richard Blumenthal (D-Conn.), initially signed on as a sponsor of the NRA-supported background check bill. Blumenthal said he had no direct contact with the NRA when he signed on to the measure but had been drawn by the idea of a bipartisan initiative to improve background checks.

On Friday, Blumenthal withdrew his support, saying in an interview that he was no longer comfortable with the bill because of “serious unintended consequences” related to provisions governing the mentally ill.

The NRA strategy has stretched into the states, as well. For instance, the group dispatched a lobbyist to Minnesota for much of the past three months because lawmakers there were considering expanded background checks and other measures.

Spurred by e-mail alerts from the group, NRA members and other gun rights activists jammed legislative committee rooms, deluged lawmakers with e-mails and phone calls — and succeeded in killing proposals that were once widely expected to pass.

“I was sabotaged by the NRA,” said state Rep. Michael Paymar, a St. Paul Democrat who authored the gun-control package he thought had a good shot at passing the liberal state House and Senate.

The Minnesota measures had been supported by the White House, with President Obama paying a visit in January and Vice President Biden calling legislators in March.

But their efforts were not enough to counteract gun rights advocates. NRA alerts warned that the background checks proposal would result in increased costs and could lead to the establishment of a government gun registry, while achieving no provable reduction in the crime.

Republican state Rep. Tony Cornish said he received 2,897 e-mails about the bills while they were being considered last month. “Only five were in favor,” he said.

Now, the legislation gathering the most support in Minnesota is an NRA-backed bill, similar in some ways to the one being pushed by the group in Congress, designed to improve reporting of mental illness.

In Congress and in some states, the NRA has already found ways to expand gun rights in the months since Newtown. The group successfully won congressional approval for new rules to ease importation of firearms that contradicted what Obama requested in the January launch of his anti-violence initiative.

The most powerful case in point is the background check legislation now being co-sponsored by Begich, Sen. Mark Pryor of Arkansas — another conservative-state Democrat up for reelection next year — and Republican Sen. Lindsey O. Graham of South Carolina, who also is running next year to keep his seat.

Those co-sponsors say the bill would make technical improvements to the current background check system and allow veterans and others to regain their Second Amendment rights after recovering from mental illness. Graham said in a statement Friday that the bill would “ensure that those who have been declared an imminent danger to themselves or others aren’t legally able to obtain a firearm. I would expect overwhelming bipartisan support for our legislation.”

The NRA’s spokesman, Andrew Arulanandam, acknowledged that the group had endorsed the legislation, a rarity by the NRA in this Congress.

The measure is opposed by Mayors Against Illegal Guns, the gun-control group led by New York Mayor Michael Bloomberg (I), and an organization of big-city police chiefs. They say the measure provides no improvement to the current background check system and allows some categories of the mentally ill to have access to weapons.

The director of Mayors Against Illegal Guns, Mark Glaze, said the legislation is so troublesome that supporters “are going to have questions to answer when, God forbid, another mass shooting happens.”

Glaze said the measure reflected a move by the NRA to provide political cover for lawmakers wanting to oppose new gun restrictions but wary of the state of public opinion. “The NRA realizes that they cannot force allies to vote against a background check bill, a measure that has a 90 percent approval rating,” he said.

The NRA-backed measure appears to be gaining steam as an alternative to the near-universal background checks proposed by Democratic leaders.

The NRA’s success comes amid an onslaught of expensive television ads purchased by the Bloomberg group. The ads targeted several swing-state senators, including Pryor.

Some gun-control advocates wonder whether the Bloomberg ads — coupled with aggressive proposals by Democratic senators and state lawmakers to ban assault weapons and impose other restrictions — have helped feed NRA warnings to its members that their gun rights were in danger.

Rep. Mike Thompson (D-Calif.), a hunter and gun owner who had been tasked by party leaders to design a strategy to woo NRA members into backing gun-control measures, said in an interview that his efforts have been frustrated in part by overreaching from the left. Some of the people he had hoped to win over now recite the NRA’s oft-broadcast concerns about government intrusion into the private rights of citizens. Thompson said a new ammunition tax and record-keeping proposal moving in the California Legislature is giving even his constituents pause.

“I have to have three meetings today with gun owner constituents who are livid about what the state is proposing,” he said.

Alice Crites contributed to this report.