Using their razor-thin majority, Republicans ended the session after 90 minutes and referred the gun control questions to a state crime commission, which it asked to present a report on the issue a week after Election Day.

“We’re much better off in a less political atmosphere to come back after the election and consider a comprehensive solution,” said Kirk Cox, the speaker of the state House of Delegates.

Now Mr. Cox and Mr. Hugo are the top targets for Democrats and gun control proponents. Both represent suburban districts long in Republican control where voters have rejected the party in the Trump era.

“This will be the first thing on the docket,” said former Gov. Terry McAuliffe. “People are fired up. People are sick and tired of saying, ‘My thoughts and prayers are with you,’ and they want action.”

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The Everytown for Gun Safety Action Fund, the political arm of Mr. Bloomberg’s gun control organization, said this week that it would invest at least $2.5 million in Virginia before Election Day — more than it spent in either of the last two legislative elections there. The group polled 14 legislative districts this week to determine how it will allocate its funds.

“Virginia is a bellwether state and we are going to be there,” said John Feinblatt, Everytown’s president. “There is no doubt this is a test. This is the next theater for what’s going to happen everywhere in 2020.”

With its odd-year elections, Virginia has a long record of serving as a leading indicator for national contests the following year. The state’s voters in 2009 were the first to reject Democrats in the Obama era, foreshadowing the rise of the Tea Party, and did the same to Republicans in 2017 following President Trump’s election. That year, Democrats swept out a generation of long-tenured suburban Republican lawmakers while coming within a coin flip in a tied race of winning control of the state’s House of Delegates for the first time since 1999.