After a failed Senate vote on the "skinny" stimulus bill last week and President Trump's unexpected announcement of support this week, a further step toward a second round of stimulus may have to be taken by House Speaker Nancy Pelosi (R-CA).

Formal negotiations between Democrats and Republicans on the size and shape of a second stimulus package stalled in August, but moderate lawmakers have recently begun pressuring party leaders to move forward.

A bipartisan group in the House of Representatives called Problem Solvers recently proposed a $1.5 to $2 trillion package.

As the Washington Post suggests, Pelosi must decide whether to negotiate with the White House to reach an agreement or stick to her longstanding demand for a $2.2 trillion agreement and hope Republicans will concede.

The House passed a $3.4 trillion budget bill (the HEROES Act) in May, and Democrats have already agreed to concede $1.2 trillion in summer party talks.

So far, The Hill reports that Pelosi has no intention of making further concessions.

"When we go into negotiations, it's about the allocation of resources," she told reporters on Thursday. 'But it's hard to go any lower when there are greater needs.'

The Senate's latest deal, a $500 billion "skinny" bill that would provide reduced federal unemployment benefit subsidies but no stimulus checks, failed to move forward after a procedural vote last week.

The proposal is mostly symbolic, and at this point the Senate may simply bow out and send members home to campaign until Election Day.

On the House side, the bipartisan Problem Solvers Caucus bill would re-send direct payments to eligible Americans, resume supplemental federal unemployment benefits at $450 per week, and provide relief to state and local governments.

Both of the latter two items are lower than the levels contained in the Democratic HEROES Act, but much more than what is provided in the HEALS Act, a competing Republican bill. The bill was introduced in the Senate at the end of July, but no one has yet voted for it.

The amount of the problem-solving bill has not yet been determined, as the end date for unemployment compensation has not been finalized; Politico reports that Pelosi's allies have already rejected the deal, and it is unclear whether it will come to a vote.

Treasury Secretary Steven Mnuchin has indicated that his administration would support a $1.5 trillion bill, and President Trump this week urged Republicans to aim for a "higher number." From Pelosi's perspective, her steady strategy may appear to be working.

"It's great," Pelosi said by phone with Mnuchin on Wednesday, according to Post sources. Referring to Trump, she added, "Call me when he gets to $2.2 trillion."