It would have extended the $600 employment insurance.
Before talks broke down late Thursday, lawmakers on both sides unsuccessfully attempted to pass their own proposals to extend the benefit and other measures.
"I'm hoping we'll make progress and I think we will", Pelosi said as she entered the Capitol.
President Trump speaks during a news conference Thursday at the White House.
In a meeting on Thursday night between top White House officials and congressional Democratic leaders, negotiations focused on an extension of the $600 per week in federal unemployment benefits, which Americans who lost jobs because of the health crisis have been receiving in addition to state jobless payments.
Democrats want a wide-ranging economic stimulus bill that would include about US$1 trillion in aid to state and local governments experiencing plunging revenues during the economic downturn.More news: Remember These Names: Meet the Stars From Beyoncé's Black Is King
"We just don't think they really understand the gravity of the problem", Schumer added.
The two sides were scheduled to meet in Pelosi's office Saturday morning, aides said.
In some of her toughest criticisms so far, she said that Republican delays on legislation and "distortions" about the pandemic "has caused death unnecessarily".
An aide familiar with the talks said Pelosi rejected an administration offer of a four-month extension of the benefit at $400 per week, combined with additional provisions for particularly hard-hit businesses and a shield against lawsuits for businesses, schools and other entities that reopen as the pandemic continues to rage. Some conservatives have refused to back any new spending, and the Republican proposal unveiled this week would slash the federal benefit to $200 per week.
On Friday, Trump took to Twitter to explicitly endorse extending the $600 payment and to criticize top Senate Democrat Chuck Schumer. Any short-term jobless benefits extension of less than $600 per week is likely to be a non-starter with them.
Those four offers have been "rejected", he said, adding that he's "disappointed" Democrats are playing politics.More news: Young Kids Could Spread COVID-19 as Much as Older Children, Adults
Talks on the relief bill are at a standstill with few reasons for optimism despite sweeping agreement among Washington's top power players that Congress must pass further relief in coming days and weeks.
"And so you have no synergy between the Republican president and the Republican Senate, and they are locked into indecision", he said.
House members left Washington yesterday, although they were told they could be called back with 24 hours' notice for votes during August.
Republicans want a smaller relief plan than one passed by the Democrat-controlled House of Representatives. But as the pandemic has worsened in past weeks - and as fractures inside the GOP have eroded the party's negotiating position - Republicans displayed some greater flexibility.
The Republican Senate Majority Leader Mitch McConnell sent senators home for the weekend without reaching a deal.
Meadows accused Democrats of politically-motivated stalling. Among the issues sure to gather momentum is a Democratic demand for a 15 percent increase in food stamp benefits.More news: IPL 2020: Franchises Want Clarification About Squad Strength
'I would say on certain issues we made progress. Debbie Stabenow of MI, the top Democrat on the Senate Agriculture Committee.