The Senate has given up on its August legislative session without any agreement on a new COVID-19 relief bill as jet fumes — leaving town in Senate parlance — have overtaken any hope for a bipartisan deal.

“If the speaker of the House and the minority leader of the Senate decide to finally let another rescue package move forward for workers and for families, it would take bipartisan consent to meet for legislative business sooner than scheduled,” Senate Majority Leader Mitch McConnell said Thursday.

The reality is that any senator, including the roughly 20 members of McConnell’s own conference who are of the belief that enough action has already been taken to respond to the pandemic’s economic consequences, could block action before Labor Day.

While no deal between the Trump administration and Speaker Nancy Pelosi of California and Senate Minority Leader Charles E. Schumer is expected any time soon, the formal move to perfunctory Senate sessions is just further evidence little is expected to happen.

Under the agreement announced on the floor, the Senate is functionally gone until 3 p.m. on Tuesday, Sept. 8, which is the day after Labor Day. The Senate would likely have been out of session the next two weeks in any case because of the Democratic and Republican political conventions. But since the pandemic has rendered those events largely virtual, it’s unlikely that would be a hindrance to meeting, either.

Until then, there will only be brief pro forma sessions, allowing the Senate to fulfill its constitutional responsibility to meet while blocking President Donald Trump from making any recess appointments.

“As has been the case, the senators would receive at least 24 hours notice before any unanticipated votes,” McConnell said. “The American people need more help, coronavirus is not finished with our country, so Congress cannot be finished helping our people.”

The majority leader moved to limit debate on a number of Trump’s judicial nominations before shutting down the floor, meaning that the scheduled business on the floor after Labor Day will be another steady drumbeat of the president’s picks for lifetime appointments to the federal bench.

The Senate completed routine business prior to effectively adjourning for the rest of the regular August recess.

First in line for a cloture vote and confirmation when the Senate returns is the nomination of Brett H. Ludwig to be U.S. district judge for the Eastern District of Wisconsin. The Ludwig confirmation will be followed by votes in relation to these nominees:

• Christy Wiegand to be a U.S. district judge for the Western District of Pennsylvania.
• Hala Jarbou to be a U.S. district judge for the Western District of Michigan.
• Thomas Cullen to be a U.S. district judge for the Western District of Virginia.
• Diane Gujarati to be a U.S. district judge for the Eastern District of New York.

Jacob Metz contributed to this report.