President Trump signed the $484 billion pandemic relief package into law on Friday, but even before the ink was dry lawmakers had already shifted their focus to the next phase of stimulus legislation as the U.S. coronavirus death toll climbed past 50,000.

The new battle has begun: House Speaker Nancy Pelosi told reporters Friday that a fifth package would be ready before long — and, though she did not put a price tag on it, she reportedly said it will be “expensive.”

Bloomberg News reports: “House Speaker Nancy Pelosi is gathering a long and expensive wish list from her fellow Democrats that would expand the social safety net as well as provide $500 billion to struggling state and local governments.” The total size of the stimulus package reportedly could run into the trillions.

Pelosi reportedly also warned that, despite Senate Majority Leader Mitch McConnell’s resistance to providing more money to state and local governments, “there will not be a bill” without such aid. Senate Democratic Leader Chuck Schumer, meanwhile, said Friday that he is seeing “more momentum” for providing assistance to state and local governments. “[McConnell] is isolated. Republican senators, Republican governors have denounced him,” Schumer said in an interview with National Public Radio. “I hope McConnell comes to his senses, turns around and helps us get state and local. But if he doesn’t, I think there will be the momentum to defeat him.”

What the White House wants in the coronavirus stimulus: Before we get to the details, we’ll point out this remarkable line from Politico’s Jake Sherman and Anna Palmer: “You don’t have to pay much attention to what the president says about what he wants in this bill, since Congress and Treasury Secretary Steven Mnuchin just got nearly $3 trillion in spending done without any meaningful engagement from him.”

That said, the administration is looking for three broad elements in the package, Sherman and Palmer report: “some sort of infrastructure measure, a tax break of some variety and policies that would help bring manufacturing back from China. Republicans both on Capitol Hill and in the White House view aid to state and local governments as the leverage point to achieve their policy goals.”

But the grand plans for $2 trillion in infrastructure spending are reportedly seen as infeasible right now, leaving the White House focused on a smaller but potentially bipartisan plan to boost 5G cellular technology and broadband access. And the administration’s idea for a payroll tax cut still faces stiff resistance in Congress. On China, the White House reportedly is looking to bring the manufacturing of PPE, drugs and other critical infrastructure back to the United States and may back tax breaks for companies that move toward that goal.

On the other hand, a big infrastructure package may not be dead yet. “If you’re spending another trillion dollars, unpaid for, Republicans would rather spend it on infrastructure than on direct aid to prop up states,” a senior Senate GOP staffer told Reuters.

How quickly will Congress move? Pelosi reportedly told Democrats this week that the legislation is nearly done and she has said it must happen “as soon as possible.” House Majority Leader Steny Hoyer told reporters Thursday that the goal is to complete the package by May 4 and vote shortly after that. But the Trump administration and congressional Republicans reportedly say they have weeks until serious negotiations start. “There is a risk that the effort to write a comprehensive rescue bill gets bogged down for months or falters given how far apart both parties are now as well as the increasingly bitter exchanges over what should come next and who will be to blame if the economy doesn’t rebound,” Bloomberg’s Laura Litvan, Erik Wasson, and Steven T. Dennis write.

But if the small business assistance Trump signed into law on Friday runs out in days, as many expect, any push for additional small business bailouts could give Pelosi fresh leverage to demand aid for states.