Meanwhile, congressional Republicans — who are wary of any new gun restrictions but have been under public pressure for weeks to do something in response to the tragedies — are going on the ­offensive, highlighting comments from former congressman Beto O’Rourke of Texas at Thursday’s Democratic presidential debate when he vowed to seize assault weapons from gun owners through a mandatory buyback program. At the House Republicans’ annual retreat in Baltimore on Friday, House Conference Chairwoman Liz Cheney (Wyo.) said talk of gun confiscation will “absolutely” motivate people to vote Republican.

The primary focus remains on the White House, where weeks have passed since a pair of mass shootings in El Paso and Dayton, Ohio, galvanized public pressure for new gun measures that have since been prioritized by congressional Democrats. The White House is looking into a number of ideas, including a version of expanded background checks and additional resources for addressing mental health issues. Attorney General William P. Barr has been drafting legislation that would expedite the death penalty for people accused of mass shootings — although questions have been raised about how much of a deterrence that would be given that the perpetrators of mass shootings often expect to be killed in the massacre.

But even people close to the White House, including those who have spoken to the president frequently on potential gun measures, remain unsure of what Trump will embrace. Shortly after he was briefed by advisers on potential policy options Thursday, Trump told reporters at the White House that a “lot of progress was made” but gave no specifics. Whether he would support expanded background checks was up to Democrats, he said.

Privately, the White House has floated at least one particularly unorthodox idea: an app connected to the National Instant Criminal Background Checks system that could be used to conduct background checks on private gun sales, according to three senators and other officials familiar with the proposal who spoke on the condition of anonymity because the proposals have not been finalized.

In turn, lawmakers and congressional aides have pointed out to the White House potential flaws in the proposal, such as security issues with the app and how it would affect how law enforcement officials access records on gun ownership. Senate Majority Whip John Thune (R-S.D.), who said he had been told of the idea by one White House official, raised concerns about gun owners’ personal data being so freely available on a handheld device, and said it “would kind of be a de facto registry.”