As Congress tries to hash out a stimulus package potentially worth more than $1 trillion, Democrats are gearing up for a fight over whether direct payments to Americans struggling with the economic fallout of the coronavirus pandemic will be enough.

Senate Minority Leader Chuck Schumer is among those arguing for expanded unemployment insurance as a source of relief.

"A single $1,000 check would help someone pay their landlord in March but what happens after that?" the New York Democrat said on the chamber floor Wednesday. "A thousand dollars goes by pretty quickly if you're unemployed. In contrast, expanded unemployment insurance — beefed-up unemployment insurance — covers you for a much longer time and would provide a much bigger safety net."

An aide for Schumer did not immediately answer whether the senator opposed to the concept of direct payments entirely, or just the form currently outlined.

President Donald Trump on Wednesday signed a $100 billion coronavirus aid package into law. The measure includes provisions for emergency paid leave for workers as well as free testing for COVID-19. Congress is now racing to put together a much broader package that could to get relief into the hands of American businesses, workers and those who are sick or out of a job. A senior administration official told CNBC a bill could be released Thursday.

As part of the administration's initial suggestions, the package could include two rounds of direct payments to taxpayers totaling $500 billion. Senate Republicans are still figuring out their own proposal, but some in the GOP, including Utah Sen. Mitt Romney, have already promoted the idea of direct payments.

The debate over direct checks and unemployment insurance comes as Congress must weigh the balance of extreme measures in extraordinary times against instituting new policy that could set a precedent historically opposed by their respective parties and backers. Some Republicans have historically opposed more government intervention, like unemployment aid. A debate over paid leave similarly divided Congress in the second round of legislation that just passed.

Schumer told CNN on Wednesday night he has spoken with Treasury Secretary Steven Mnuchin twice about the third bill. He previously criticized Senate Majority Leader Mitch McConnell for working only with the administration on the initial package proposal, excluding House and Senate Democrats.

"I know some of the things they're interested in. Some of the things we're interested in. A lot of them overlap, and there are some things that we're going want," Schumer said of his conversation with Mnuchin.

"The one thing I did tell him as well, though, if there are going to be some of these corporate bailouts, we need to make sure workers and labor come first. That people are not laid off. That people's salaries are not cut," Schumer said. "If these big companies, many of which did buybacks, the airlines I think did about [$45] billion of stock buybacks, they have to put their workers first if they're going to get this help."

The administration is looking to set aside as part of its package $50 billion for the ailing airline industry, as well as $150 billion for "other distressed sectors." Trump has said the cruise and hotel industries are particularly feeling the pain. Trump himself owns a hotel and resort business.

Beyond Schumer, other Democrats have already made clear they will push for concessions and protections for workers along with any corporate aid. An initial aid package to the airline industry after 9/11 controversially did not have protections for workers.

Sen. Elizabeth Warren, D-Mass., has proposed her own comprehensive bailout package, that would require any company taking federal money to maintain payroll for a period of time, and forbidding them from buying back stock permanently.

– CNBC's Eamon Javers contributed to this report.