WASHINGTON (NewsNation Now) — A top House Democrat said no vote on federal coronavirus relief is expected in his chamber this week as negotiations continue. Any package approved by lawmakers is expected to contain a new round of direct relief payments to Americans.

House Majority Leader Steny Hoyer said it’s possible House members will be called back later in the month to vote if an agreement is reached.

Though headlines that conversations between negotiators around relief might sound optimistic, Washington insiders warned a deal this close to Election Day is highly unlikely.

Over the weekend, Pelosi dismissed the latest White House offer as “one step forward, two steps back.”

Last week saw a back-and-forth on negotiations over a relief package.

On Friday, the White House boosted its COVID-19 aid offer to roughly $1.8 trillion, with a key state and local fiscal relief component moving from $250 billion to at least $300 billion. The White House says its most recent prior offer was about $1.6 trillion.

“I would like to see a bigger stimulus package than either the Democrats or Republicans are offering,” Trump said on Rush Limbaugh’s radio show Friday, which his campaign called a “radio rally.”

Earlier this week, Trump criticized Democrats for their demands on an aid bill. On Tuesday, he ordered an end to the weekslong talks after being told that few Republicans in Congress would end up voting for a possible deal between Pelosi and Treasury Secretary Steven Mnuchin.

After that decision, Trump sought to revive the negotiations Thursday. Yet as Mnuchin was reengaging with Pelosi, staffers in the White House — working under chief of staff Mark Meadows, a key negotiator — were issuing demands for a smaller package that includes Trump’s priorities.

Democrats have made it clear they will not do a piecemeal approach until the Trump administration signs off on a broader, comprehensive plan they are proposing for virus testing, tracing and other actions to stop its spread. They have scaled back a $3 trillion measure to a $2.2 trillion proposal.

GOP Senate Majority Leader Mitch McConnell told an audience in Kentucky that he doesn’t see a deal coming together soon out of a “murky” situation in which the participants in the negotiations are elbowing for political advantage.

“I’d like to see us rise above that like we did in March and April but I think it’s unlikely in the next three weeks,” McConnell said. McConnell said later that “the first item of priority of the Senate is the Supreme Court,” suggesting there isn’t time to both process a COVID-19 relief bill and the nomination of Judge Amy Coney Barrett before the election.

The Associated Press contributed to this report.