Speaker Nancy Pelosi (D-Calif.) on Thursday rejected a push by some House Democrats to vote this weekend on standalone legislation to extend federal unemployment insurance payments that expired at the end of July, maintaining that it could undermine negotiations on other aspects of a coronavirus relief package.

More than 100 Democrats this week signed on to a letter spearheaded by Reps. Scott Peters (Calif.), Derek Kilmer (Wash.) and Don Beyer (Va.) that urged leadership to schedule a vote for Saturday on legislation to extend enhanced unemployment insurance on a time frame based on econometrics.

Pelosi said that she personally supports the idea of tying unemployment insurance payments to economic measures like the unemployment rate instead of allowing the benefits to expire on arbitrary dates. But she argued that voting on such a proposal at this stage could ultimately backfire in coronavirus relief negotiations.

"That's a very positive initiative. I have encouraged that, I have welcomed that suggestion," Pelosi said during an interview on "PBS NewsHour."

"I don't think strategically it's where we should go right now, because the Republicans would like to pass something like that and say forget about it," Pelosi continued. "Forget about state and local [government funding], forget about our investments in stopping the virus, forget about other initiatives that feed the food insecure children in our country, vote by mail initiatives and the rest."

Pelosi also warned that if the House were to pass a standalone bill to extend unemployment insurance, Senate Republicans could amend it and add "poison pills." 

"I don't think it's done by giving them an out," Pelosi said of reaching a coronavirus aid deal with Republicans. "I think it's done by making them come into the negotiation."

Pelosi reiterated her stance in a letter to colleagues late Thursday night while noting that “the ideas Members have put forth have been excellent.”

“However, we must consider their timing and strategic value. They cannot come at the expense of addressing the priorities of the Heroes Act — particularly support for our heroes in state and local government and education, who are in crisis,” Pelosi wrote, referring to the sweeping $3 trillion coronavirus aid package that House Democrats passed in May. 

That bill, which Senate Republicans have declined to consider, would extend the $600 weekly unemployment supplement through January 2021. 

The bipartisan negotiations between Pelosi, Senate Minority Leader Charles Schumer (D-N.Y.), Treasury Secretary Steven Mnuchin and White House chief of staff Mark Meadows collapsed earlier this month, primarily over funding for state and local governments, aid to help schools reopen and the size of the weekly federal unemployment insurance payments.

Democrats want to renew the payments at the previously established level of $600 per week, while Republicans called for a lower amount. President Trump signed an executive order earlier this month designed to provide an additional $400 per week, but the actual weekly payment will drop to $300 in cases where states lack the budgets to supply an additional $100 in the way the program was intended. 

House Democrats, particularly vulnerable members in swing districts, have been growing anxious over the weeks-long stalemate that has dragged on after the unemployment insurance payments ended last month. 

"While there are various proposals to extend unemployment benefits, the only way to provide financial relief to millions of Americans without being subject to political hurdles, is to enact automatic stabilizers for unemployment benefits," lawmakers wrote in the letter spearheaded by Peters, Kilmer and Beyer.

"By passing legislation that ties unemployment benefits to economic triggers, we can ensure that aid is restored to those who need it and prevent future lapses as long as the economy tells us aid is needed," they wrote. 

The House is currently scheduled to vote Saturday on legislation to prevent any operational changes at the Postal Service that could affect mail delivery during the COVID-19 pandemic and provide $25 billion for the agency's operations. 

House Democrats opted to hold the vote on Saturday so that it wouldn't conflict with the party conventions happening this week and next.

Democrats have conducted proceedings virtually for their party convention this week, rather than the four-day event they originally envisioned in Milwaukee with throngs of delegates gathering together.

Pelosi said in the PBS interview that she thinks conventions in the future will be a combination of virtual and in-person proceedings.

"I think our future is probably a hybrid, because this was great. It had impact, it had succinctness, it had clarity, but it didn't have our collaboration of seeing each other, which I still think is something very important to the strength of the party. But if I had to choose one way, actual or virtual, I would choose virtual. But I think hybrid is the wave of the future where we can have the benefit of both," Pelosi said. 

This story was updated at 10:31 p.m.