“We are not taking these additional actions simply to respond to mass shootings,” said Representative Jerry Nadler, Democrat of New York and the committee chairman, adding, “We are acting because of the urgent need to respond to the daily toll of gun violence in our communities, whether they are mass shootings or not, whether or not they make headlines.”
But Representative Doug Collins of Georgia, the senior Republican on the committee, said each of the bills would infringe on Americans’ Second Amendment rights, and he raised “serious due process problems” with the red flag law.
The central figure in the debate, though, remains Mr. Trump. The president’s statements on gun safety have been “all over the lot,” Mr. Schumer said on Monday.
The president initially expressed support in early August for “very meaningful background checks” after deadly mass shootings in El Paso and Dayton, Ohio, but stopped short of endorsing the bill passed by the House. Then, as has been his pattern, Mr. Trump’s resolve appeared to weaken after talks with gun rights advocates.
Senate Democrats involved in the White House talks said it remained unclear what Mr. Trump might accept.
“It’s encouraging — they’re still talking,” said one of those Democrats, Senator Joe Manchin III of West Virginia, who was a chief sponsor of a background check bill that fell to a Senate filibuster in 2013.
But Senator Christopher S. Murphy, Democrat of Connecticut, who is also involved in the talks, said he was concerned the effort could collapse if Republicans demanded a package of measures, as opposed to a stand-alone vote on a background check bill.
“I’ve expressed my worry to the White House the package could get so big that it could all fall apart,” he said.