On Friday morning, Donald Trump said, on Twitter, “Serious discussions are taking place between House and Senate leadership on meaningful Background Checks. I have also been speaking to the NRA, and others, so that their very strong views can be fully represented and respected.” In a second tweet, Trump added, “I am the biggest Second Amendment person there is, but we all must work together for the good and safety of our Country. Common sense things can be done that are good for everyone!”

Trump isn’t the only Republican talking up the possibility of expanding the current system of background checks for gun purchases. For months now, Mitch McConnell, the Senate Majority Leader, has been sitting on a universal-background-checks bill that passed the House of Representatives. During a radio interview in his home state of Kentucky, on Thursday, McConnell rejected Democratic demands for an immediate recall of the Senate from its summer recess. However, McConnell also said that the issue of background checks would be “front and center” when Congress reassembles on its regular schedule, in September. “The President called me this morning about this,” McConnell added. “He’s anxious to get an outcome, and so am I.”

We have been here before, of course. Early last year, after the massacre at Marjory Stoneman Douglas High School, in Parkland, Florida, Trump called for universal background checks and raising the age limit for purchasing rifles. Shortly after having dinner at the White House with the leaders of the N.R.A., however, he abandoned these proposals, citing a lack of political support. This humiliating retreat demonstrated that Trump, despite his popularity with Republican voters, wasn’t strong enough, or determined enough, to break the N.R.A.’s veto over gun policy.

In recent days, commentators and Republican political strategists have offered a number of reasons that things may be different now. For starters, opinion polls show overwhelming public support for enhanced gun-control measures, including the elimination of loopholes in the current background-check system, which doesn’t apply to unlicensed gun sellers. In a Morning Consult/Politico poll taken this week, eighty per cent of respondents, including seventy-four per cent of Republicans and people who lean Republican, said that they strongly support requiring background checks on all gun sales. (The figures are even higher if you include people who said that they “somewhat support” universal checks.) “I think we’ve reached a tipping point,” Scott Jennings, a political adviser to McConnell, told the Times. “The polling clearly supports that notion, and as long as the president is going to be for something, I think there will be momentum for it within the party.”

The N.R.A. has consistently opposed strengthening background checks, and almost all other gun-control proposals, of course. In a statement issued on Thursday, Wayne LaPierre, the longtime head of the organization, declined to comment on his “private conversations with President Trump,” but he did say that “the NRA opposes any legislation that unfairly infringes upon the rights of law-abiding citizens. The inconvenient truth is this: the proposals being discussed by many would not have prevented the horrific tragedies in El Paso and Dayton.”

This response was eminently predictable, but the N.R.A. is facing a dual challenge to its grip on Capitol Hill. Internally, the organization is in turmoil, with supporters and board members questioning the lavish spending being done by LaPierre and other senior executives. After the Parkland shooting, according to a report in the Washington Post, LaPierre tried to get the N.R.A. to buy him and his family a 6.5-million-dollar, ten-thousand-square-foot mansion in a Dallas gated community, because he needed somewhere more secure to live. Last week, three members of the N.R.A.’s board of directors quit. In a resignation letter, they said, “Our confidence in the NRA’s leadership has been shattered.”

Externally, the N.R.A. is also under fire. The office of the New York attorney general is investigating the organization’s tax-exempt status. And, in many parts of the country, a reënergized and well-financed gun-control lobby has challenged it politically, and even outspent it during the 2018 midterms. “I’ve never seen them weaker,” John Feinblatt, the president of the advocacy group Everytown for Gun Safety, told USA Today. “I think they have been very much sidelined.”

That sounds encouraging. Still, as Trump decamps for the Trump National Golf Club in Bedminster, New Jersey, there are plenty of reasons to remain skeptical, beginning with the calendar. The usual pattern, which the N.R.A. and other opponents of gun control rely on, is for the political momentum behind gun-control efforts to ebb as memories of the latest atrocity recede. Congress isn’t due back until September 9th, which is a full month away.

Also, it is Trump we are dealing with, and he is notoriously averse to crossing rural and suburban gun owners, who make up a key part of his base. Even if the polls currently show overwhelming support for expanded background checks and other measures, Trump will be sensitive to a possible backlash, especially if the opposition includes some of his right-wing media outriders, such as Sean Hannity and Rush Limbaugh.

Furthermore, there is a possibility that Trump will try to tie any gun-control measures he endorses to immigration-law changes that Democrats oppose, such as lengthening the period for which asylum-seeking families can be detained after crossing the border. In a tweet on Monday, Trump suggested “marrying” immigration and gun control. On Thursday, the Times reported that he has told some advisers that he “would like a political concession in exchange” for acting on gun control. If he insists on this linkage, the chances of getting any legislation passed are slim.

Finally, Trump has already passed on the most urgent need in the issue: a restoration of the Clinton-era ban on assault weapons, which mass shooters used, in the span of a week, in El Paso, Texas; Dayton, Ohio; and Gilroy, California. During a back-and-forth with reporters on Wednesday, Trump said that “there is no political appetite for it from the standpoint of the legislature.” He made this statement even though, for years, polls have consistently shown that most Americans favor restoring the ban on assault weapons, which a G.O.P.-controlled Congress allowed to expire, in 2004. In this week’s Morning Consult/Politico poll, seventy per cent of all voters, and fifty-four per cent of Republicans, expressed “strong support” or “some support” for prohibiting such weapons. Among Republican women, the support level was at sixty-four per cent.

The public is ahead of the political system. Tightening up background checks would help prevent criminals from purchasing guns. Expanding so-called red-flag laws would help families and judges to disarm some people who are clearly disturbed. But many of the individuals who have carried out gun massacres bought their weapons legally, or got somebody else to purchase them. Often, family members and friends don’t identify shooters as serious threats prior to their rampages. (On Friday, the Times reported that the mother of the shooter in El Paso did express concerns to police about her twenty-one-year-old son purchasing an AK-47 assault rifle, but she declined to identify herself or him.) As other countries have demonstrated, by far the most effective way to keep assault weapons out of the hands of these individuals is to ban their sale in the first place. That isn’t going to happen.