White House economic adviser Larry Kudlow said on Wednesday it was a "sunny, optimistic" morning in terms of negotiations on a coronavirus relief bill with House of Representatives' Democratic leaders.

"It's a bit cloudy down here in terms of the weather, but I think there's a relatively sunny, optimistic morning in terms of the negotiations," Kudlow said on CNBC. "Things are moving in a favorable direction. I can't promise anything, but things are getting better, looking better for this," he said.

President Donald Trump said Tuesday he was willing to accept a large aid bill despite opposition from his own Republican Party.

With just two weeks until the U.S. presidential election, Trump signaled a willingness to go along with more than $2.2 trillion in new COVID-19 relief, a figure Democrats have been pushing for months.

Senate Majority Leader Mitch McConnell, a Republican, publicly said he would bring up a deal if one is reached by Treasury Secretary Steven Mnuchin and Democratic House Speaker Nancy Pelosi and approved by the House of Representatives.

But he provided no timetable and privately has told his fellow Republicans that he did not favor a deal before the Nov. 3 presidential and congressional elections, a senior Senate Republican aide told Reuters.

Holding a vote on a costly new package of aid could prove politically difficult for some Senate Republicans running for re-election in conservative states.

Nonetheless, Trump, whose prospects for re-election are in doubt, tacked in the opposite direction.

"I want to do it even bigger than the Democrats," Trump said in an interview with Fox News, as talks between Pelosi and Mnuchin continued.

Pelosi, speaking to reporters after a mid-afternoon call with Mnuchin, was asked about prospects for a legislative package by the end of this week. "I hope so. That’s the plan," she said.

In a letter to her fellow Democrats on Tuesday evening, however, Pelosi made no mention of wrapping up the battle by week's end. "I remain hopeful that we can reach an agreement before the election," she wrote.

Pelosi's deputy chief of staff, Drew Hammill, said that a 45-minute call between the speaker and Mnuchin was productive "as they move closer to an agreement."

Hammill said on Twitter that negotiations would continue on Wednesday.

The White House has proposed $1.8 trillion in coronavirus relief, while Pelosi is pushing for $2.2 trillion.

In an interview with Bloomberg TV, Pelosi said aid to state and local governments and Republican demands for liability protection for businesses remain sticking points. But she suggested the Democrats could find grounds to agree on liability protections if the administration agrees to eliminate certain language sought by McConnell that she believes would overshadow protections for workers.

Senate Republicans have repeatedly stated their opposition to additional COVID-19 relief spending near the $2 trillion mark, focusing instead on smaller initiatives. As negotiations heated up, several were wary, non-committal or just plain negative about aid totaling $1.8 trillion or more.

"I think it's very unlikely that a number of that level would make it through the Senate, and I don't support something of that level," Senator Mitt Romney told reporters. "Something far more targeted to the people who really need help, I'd like to see done, and I'd like to see done as quick as possible."