Louisiana Gov. John Bel Edwards can call a special election to fill any congressional seat vacated in the state.
The House passed a measure to increase the size of stimulus checks to $2,000 with a vote of 275-134.
The measure now passes to the Senate over objections from some House Republicans.
Trump, under pressure, signs $900 bn Covid relief bill
President Donald Trump on Wednesday urged Congress to increase the amount of stimulus checks from $600 to $2,000.
US Congress fails to agree to boost stimulus checks
Democrats had thrown their weight behind the proposal to increase direct aid to Americans.
Trump throws pandemic relief into doubt
The veto of the $740 billion measure to fund the military for fiscal 2021 came a day after Trump threw a separate $900 billion Covid-19 relief bill and overall funding for the government into question.
House Democrats said they already have amended legislation that would send larger stimulus checks to individual taxpayers.
Trump rejects Covid relief bill, calling it 'a disgrace'
US Congress approves $900 billion stimulus package
The latest stimulus measure as proposed would supplement state unemployment insurance with $300 a week and send another $600 to individual taxpayers.
US Congress reaches deal on Covid-19 relief package
US lawmakers nearing stimulus deal amid signs of economic distress
Congress nears US spending deal, Fed more upbeat on outlook
Congress nears US spending deal with Fed to weigh in on economy
The meeting also involved top congressional leaders, such as Treasury Secretary Steven Mnuchin, Senate Minority Leader Chuck Schumer and House Minority Leader Kevin McCarthy.
Lawmakers push bipartisan US stimulus plan to break stubborn deadlock
On the prospects of passing complex legislation, Manchin warns against letting ‘perfect be the enemy of the good.’
Democrats see little to like in Trump stimulus plan
White House proposes new $916 bn stimulus plan to break deadlock