The White House wants and is pushing for the “liability shield” as a top priority but would be willing to sign off on a deal that lacks the legal protections, those people said. Senate Majority Leader Mitch McConnell (R-Ky.) controls the Senate floor and could shoot down any deal that leaves out what he has said is a necessary component of any stimulus package.

One of the people familiar with the administration’s thinking said the measure was “considered important but not absolutely essential.”

The dealmaking flexibility conflicts with the ultimatum McConnell has given Democrats that any congressional stimulus package must make it significantly harder for workers and customers to sue employers and businesses for damages related to the coronavirus.

McConnell has said that he will not bring up legislation for a vote in the Senate if it does not include the liability measure. “We’re not negotiating over liability protection,” McConnell told CNBC on Tuesday. “We’re not negotiating with Democrats over that.”