Senate Minority Leader Chuck Schumer (D-NY) speaks at a press conference at Corona Plaza in Queens on April 14, 2020 in New York City.

Staffers for Senate Minority Leader Chuck Schumer and House Speaker Nancy Pelosi will meet with the Treasury Department on Wednesday to discuss the Democrats' push to pass additional coronavirus relief legislation.

The new round of working-level negotiations between Democrats and members of the Trump administration indicates a potential thaw in the ongoing stalemate over emergency funding.

It also reflects a desire on both sides to keep the government's fiscal spigot open and pouring money into the economy, which has been devastated by the disease and the strict policies imposed to slow its spread.

The talks are set to take place as an already-passed $349 billion fund for small businesses, called the Paycheck Protection Program, is quickly being wiped out: More than 1.3 million loans had been approved by Wednesday afternoon, totaling a value of more than $296 billion, according to the Small Business Administration.

Schumer, D-N.Y., spoke with Treasury Secretary Steven Mnuchin on Wednesday morning about the "interim" relief package, a spokesman for the Senate leader's office told CNBC.

Two sources confirmed that staff members for Schumer and Pelosi, D-Calif., will meet with Treasury officials later Wednesday.

Last week, Pelosi and Schumer called for Congress to pass a bill that would include at least $500 billion in relief for small businesses, hospitals, states and food assistance programs.

Those funds would put $125 billion toward small businesses, another $125 billion for community-based lenders and Small Business Administration loans, $100 billion to bolster hospitals and community health centers, and $150 billion for state and local governments.

It is unclear whether Democrats are still pushing for all of those provisions as part of an interim bill. The Treasury Department did not respond to CNBC's request for comment on the talks.

"Democrats know that in order for the Paycheck Protection Program to succeed, it must work for everyone," Pelosi said in a statement Wednesday afternoon.

Pelosi said that Democrats have been asking the Trump administration to help the groups identified in their bill. But "as has been clear since last week, Republicans' bill which fails to address these critical issues cannot get unanimous consent in the House," Pelosi said.

Senate Democrats on Thursday blocked an attempt by Senate Majority Leader Mitch McConnell, R-Ky., to rush another $250 billion in funding for the program through his chamber by a unanimous vote.

Republicans then rejected the Democratic proposal outlined by Pelosi and Schumer.

The proposal from Schumer and Pelosi followed a $2 trillion emergency spending package, known as the CARES Act, that President Donald Trump signed in late March to try to blunt the economic destruction of the Covid-19 pandemic for individuals and businesses.

States are trying to contain the spread of the disease by enforcing strict social distancing measures, such as closing nonessential businesses and issuing statewide stay-at-home orders. While governors say their efforts are paying off, the measures have prompted an unprecedented spike in unemployment and a massive market rout.

Despite their disagreements, Republicans and Democrats both seek to add funds to the nearly $350 billion Paycheck Protection Program included in the CARES Act to help small businesses keep their employees on the payroll.

An industry source told CNBC on Wednesday afternoon that "today or tomorrow" that money is set to run out.