A $150 billion federal program designed to help states, cities and counties respond to the coronavirus pandemic has pitted some governments against one another, forcing them to scrap over the fast-dwindling, limited aid.

The fight has intensified as Congress and the White House near deadlines to decide the scope of the next round of coronavirus relief. State and local leaders have demanded between $500 billion and $1 trillion in new assistance, but the vast uncertainty surrounding the initial tranche of funding has fueled accusations that money is being misspent or hoarded.

The funds were supposed to help local governments purchase personal protective equipment, pay first responders and cover other public-health costs related to the pandemic. But restrictions in how the aid can be used, and confusion around how it is supposed to be doled out, mean that many have struggled to take full advantage of the so-called Coronavirus Relief Fund four months after Democrats and Republicans authorized it.

State officials, who largely are overseeing the program, have put aside about $18 billion exclusively to help their smallest localities, far less than some lawmakers anticipated and the Trump administration appeared to prescribe, according to a Washington Post analysis of municipal data.

“They’ve sat on this for months. They’ve cut it into pieces so there’s only a third left coming to local government,” said Brad Cole, the executive director of the Illinois Municipal League. “How do you think we feel about it?”

Many attribute the troubles to Washington, which hastily passed the Cares Act in March and did not appropriate anywhere near what states and localities had asked for. Now, the headaches threaten to add to the tensions on Capitol Hill as lawmakers resume negotiations over another coronavirus relief package. Republicans have staunchly opposed sky-high spending to help cash-starved state and local governments, but some GOP leaders believe the party’s resistance may fade as cases surge — and local infighting worsens — unleashing even more economic havoc in lawmakers’ backyards.

“I’ve always said, as people become aware of the financial straits hitting their states and towns, they would become aware of the wisdom of what we’re trying to do,” said Republican Sen. Bill Cassidy (La.), a lead author of a bipartisan bill to send an additional $500 billion to cities and states.

For four months, Democrats and Republicans in Washington have warred over the need for local aid. City and state leaders have pointed to shuttered storefronts, sharp declines in shopping and tourism, and steep drop-offs in tax revenue that have come as a result of their efforts to arrest the spread of the coronavirus.

In a sign of their desperation, they’ve even embarked on a massive lobbying blitz: Cities and counties alone have registered at least 28 lobbying firms since March just to encourage lawmakers to extend them a wide array of new coronavirus-related funding, according to a review of federal ethics forms.

But their repeated entreaties have been met with partisan bickering on Capitol Hill. A bill that honored local leaders’ requests for $1 trillion in new, easy-to-access coronavirus aid cleared the Democratic-dominated House in May, but it quickly faltered in the Republican-controlled Senate. GOP Leader Mitch McConnell (Ky.) since then has signaled the next pandemic-relief package — including funds for local governments as well as other stimulus to support businesses and families — should not exceed $1 trillion in total.

“State and local governments had to balance their budgets by the end of June,” House Speaker Nancy Pelosi (D-Calif.) told reporters last week, scoffing at McConnell’s dollar limit. “We’ve gone past the deadline but we haven’t gone past the need.”

In Kentucky, McConnell’s home state, Democratic Gov. Andy Beshear has pleaded for more help from Congress. “That’s a category that we’ll be looking at,” McConnell responded during a recent event in the state, marking a shift from months ago when he espoused bankruptcy as a potential solution. “I can’t guarantee in advance, but that is another category we’ll be looking at.”

The White House, for its part, is “open to targeted assistance for states and localities,” spokesman Judd Deere said in a statement.

Nationwide, governors in recent months have urged Washington to act. In Illinois, Gov. J.B. Pritzker (D) said the dollars so far have helped purchase masks and other equipment and support local businesses in need. But the money still can’t be used to help the state address its biggest challenge — a massive $6 billion deficit. The Trump administration also has been slow to answer states’ questions about appropriate uses for the aid, including education at a time when the president is calling on schools to reopen, Pritzker said.

“It certainly does not take care of the challenge we’re all facing,” the governor warned.

Local governments, meanwhile, say they aren’t just battling Washington for financial help — they’re also haggling with states over access to federal aid.

City leaders in Illinois anticipated they would see about $800 million set aside to help them cover their coronavirus expenses. Last month, however, state lawmakers opted to dedicate to them about a quarter of that, according to Cole, who leads the state’s municipal association. The limited funds now must be split among roughly 100 counties and 1,200 cities, leaving Illinois officials fearful about their finances as they rack up once-unthinkable coronavirus expenses.

“This is the problem when you put the county or the state in between the federal government and the city,” Cole said. “Everybody wants to keep more for themselves.”

Like other governors, Pritzker stressed the state isn’t hoarding money — but rather that it is best equipped to disburse those dollars to first responders, local businesses and other recipients on a tight deadline.

In North Carolina, meanwhile, state leaders received $4 billion under the Cares Act to cover their coronavirus expenses. But they put aside just about $300 million for counties to divvy up among themselves and more than 300 local cities and towns. The allotment has frustrated cities such as Greensboro, where Mayor Nancy Vaughan said officials expected more money — and are now “incurring significant expenses” without a clear indication about how much money they will see reimbursed.

Ford Porter, a spokesman for Gov. Roy Cooper (D), said in a statement that North Carolina is a “state-centric service state,” so its spending on health and education still stands to benefit local communities.

Some of the tensions between cities and states stem from the way the Cares Act was written. Under the total $2 trillion law, Congress dedicated $150 billion to states and their largest cities and counties. The amount was far short of what they sought, and far less than some congressional Democrats originally advocated, fearing the public-health expenses facing local governments would be vast.

Earlier this year, the Treasury Department recommended states “should” disburse 45 percent of their remaining funds to smaller cities and counties that didn’t receive their aid directly, according to guidance it released. But it offered two different methodologies for calculating the percentage in the same document, creating widespread confusion, a senior administration official acknowledged Friday, speaking on the condition of anonymity to discuss internal deliberations.

Since then, states nationwide have earmarked about 16 percent, or roughly $18 billion, exclusively for their smallest cities and counties, a Post analysis found. To compute the figure, The Post relied on data compiled as of last week by the National League of Cities, the National Association of Counties and some individual states. The U.S. government does not require states to disclose how the dollars were spent, illustrating the more wide-ranging oversight issues plaguing the whole of the $2 trillion law.

The data excludes the District of Columbia and U.S. territories that also received Cares Act support, as well as large metropolises that might have decided to aid towns within their boundaries. With larger cities and counties factored into the equation, states have shared about $45 billion, still billions less than some federal officials had envisioned.

“There’s going to be at least a $144 billion fiscal impact of covid-19 on counties. This includes both increased expenditures and lost revenue,” said Mark Ritacco, deputy director of government affairs at NACO. He said the numbers don’t “come anywhere close to giving counties the resources they need to response to covid-19.”

In other states, such as Colorado, smaller cities have been able to turn to their larger counties to obtain money to cover costs associated with the pandemic. But seeking those reimbursements at times has been fraught with difficulty. In Aurora, city leaders who want to offer hazard pay to some first responders have warred with Arapahoe County, which holds the purse strings, over whether the congressional aid can be used for those purposes.

“Their response has continued to be [that] they need more guidance from the Treasury Department,” said Jim Twombly, the city manager of Aurora. “We’re not sure what we’re going to do about that.”

A spokesperson in Arapahoe County did not respond to a request for comment.

Some governments may be delaying payments to localities, and holding onto the cash, in the hopes that Congress rewrites some of the rules so they can fix their own significant shortfalls, Republicans contend. The fears about hoarding have fueled some of the party’s opposition to sending more money to states and cities, with many saying they instead favor allowing states more flexibility to use the money they already have.

But some of the local feuds have ratcheted up the national pressure on GOP senators who are vulnerable in November’s election, including Thom Tillis of North Carolina, Cory Gardner of Colorado and Susan Collins of Maine. The three incumbents have come out in favor of enhanced state and local aid, complicating the political calculus for McConnell and the White House.

“I think colleagues will come around to this because it’s good policy,” Cassidy said, “and because it’s good policy it will be good politics.”