WASHINGTON (AP) — Congress is on the verge of passing an almost $500 billion coronavirus relief bill, but battle lines already are forming over the next measure amid growing demands to approve additional billions for state and local governments, the Postal Service and even infrastructure.

The talk of a fifth measure is running into early opposition from conservatives, chiefly Senate Republicans, who warn the spending spree cannot go on indefinitely. The GOP senators saw their request to replenish a Paycheck Protection Program nearly double in size, as Democrats persuaded President Donald Trump to support additional funding for underbanked communities, health providers and a national testing initiative.

So far, big spending is carrying the day, pushing the projected deficit for the current year past $3 trillion — more than double the previous record from the Great Recession.

The House is expected to vote Thursday on the latest, $483 billion measure, already passed by the Senate, which as its centerpiece would add $321 billion to replenish a small-business payroll fund, while pumping more money into hospitals and testing.Trump says he'll sign it into law.

Supporters of the Paycheck Protection Program warn that this week's refill may only last a few days, likely putting business groups back at Washington's doorstep, along with the nation's governors and the cash-strapped Postal Service.

House Speaker Nancy Pelosi, D-Calif., said in an interview Wednesday on Bloomberg Television that more funding for state and local governments -- there's already $150 billion allocated in last month's $2 trillion coronavirus package -- means support for "the health care worker, the police and fire, the first responders, the emergency services people, the teachers in our schools, the transportation workers who get vital, essential workers to work."

Senate Majority Leader Mitch McConnell, R-Ky., meanwhile, is testing the brakes. After Tuesday's Senate vote, McConnell said there will be a lengthy Senate debate on the next package before billions more in spending will move through his chamber.

"We haven't had much discussion about adding $2.7 trillion to the national debt, and the way that could indeed also threaten the future of the country," McConnell told conservative radio host Hugh Hewitt.

Trump has said he supports including fiscal relief for state and local government in another virus aid package along with infrastructure projects, but McConnell said the Senate is "going to push the pause button here."

Republicans are not ready to send a "blank check" to the states, McConnell said. "We all have governors regardless of party who would love to have free money," he said.

McConnell said he sees "no good reason" why laws shouldn't be changed to allow states to enter into bankruptcy proceedings, which they are now unable to do.

Such a suggestion is highly unlikely and governors delivered swift blowback.

Gov. Andrew Cuomo, who has warned New York will lose anywhere from $10 billion to $15 billion in revenues during the epidemic, called it "one of the saddest, really dumb comments of all time."

In a radio appearance Wednesday, Cuomo said: "You want to reopen the economy, Mr. McConnell, so everyone gets their job back? But the people you put in charge of reopening, the governors and the states, should declare bankruptcy?"

New Jersey Gov. Phil Murphy said: "Really? This is the time, in a moment of crisis unlike any our country has faced in at least 100 years, to suggest it's a good thing for states to go bankrupt?"

"Come on, man. That is completely and utterly irresponsible," Murphy said.

Given the It's not clear how soon the next bill can advance. There's also the question of when Pelosi and McConnell feel comfortable reopening Capitol Hill, though Trump has signaled he wants discussions to begin as soon as Congress finishes the current legislation. The Senate is scheduled to return May 4.

The Senate passed the bill by voice vote on Tuesday, and the House is expected to pass it overwhelmingly in a roll call vote Thursday.

Most of the bill's funding, $331 billion, would go to boost a small-business payroll loan program that ran out of money last week. There would be $100 billion for health care, with $75 billion to hospitals and $25 billion to boost testing for the virus, a key step in building the confidence required to reopen state economies. There is $60 billion for small-business loans and grants.

Democratic demands for additional funds for hospitals and virus testing in the states became more pressing and eventually gained support from Republicans.

Of the $25 billion for increased testing efforts, at least $11 billion goes to state and tribal governments to detect and track new infections. The rest will help fund federal research into new coronavirus testing options.

Currently, the U.S. has tested roughly 4 million people for the virus, or just over 1% of its population, according to the Covid Tracking Project website.

The centerpiece of the deal remains the small-business payroll program. It provides forgivable loans so shops can continue paying workers while businesses remain closed for social distancing and stay-at-home orders.

Launched just weeks ago, the Paycheck Protection Program quickly reached its lending limit after approving nearly 1.7 million loans. That left thousands of small businesses in limbo as they sought help.

Among the targets for the next bill is the Postal Service, which has more than 600,000 workers, mostly covered under union-negotiated contracts, but is hamstrung financially by COVID-19-related revenue losses and pension funding requirements.

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Associated Press writers Marina Villanueve in New York and Mike Catalini in Morrisville, Pa., contributed to this report.