According to the Gun Violence Archive, a nonprofit that tracks gun violence in America, there have been 283 mass shootings in 2019, defined as those in which four or more people were killed or injured, excluding the perpetrators. In August alone, 53 people died in mass shootings in the United States. Using the Justice Department’s definition of mass killings — in which at least three people die — there have been five mass killings involving firearms since the Dayton massacre last month. West Texas is the sixth.

Republicans have long been resistant to gun safety legislation, but the political landscape around the issue is changing. The N.R.A., mired in lawsuits and personnel battles, is at its weakest in decades. Outrage over mass shootings is growing and gun safety groups are ascendant, amid a wave of student activism that emerged from the 2018 mass shooting at Marjory Stoneman Douglas High School in Parkland, Fla.

The El Paso and Dayton shootings left even the most ardent Republican defenders of gun rights feeling rattled, and the party began coalescing around red flag laws. Senator Lindsey Graham, Republican of South Carolina, along with Mr. Blumenthal, is sponsoring a bipartisan measure, and Senator John Thune, the No. 3 Republican, has said he is “confident Congress will be able to find common ground” on the issue.

On Sunday, Senator Rick Scott, Republican of Florida, said the federal government should follow the model set by his home state, which passed a red flag measure after the Parkland massacre.

“We’ve got to figure this out,” Mr. Scott said on the NBC program “Meet the Press.” “We’ve got to figure out how we get guns away from mentally ill people who want to harm others or themselves.”

But for Democrats — many of whom also favor banning assault weapons and high-capacity magazines — red flag laws do not go nearly far enough. Mr. Blumenthal and others say such measures must be married with expanded background checks, at the very least, to produce meaningful gun safety improvements.