Major metropolises including Austin, Baltimore, Boston and Detroit may struggle to access a $500 billion emergency lending program meant to shore up local governments’ cash-starved budgets under rules that limit participation only to cities with 1 million or more residents.

The program, administered by the Federal Reserve in coordination with the Treasury Department, seeks to buy short-term debt from cities, which should push down interest rates and help local leaders borrow at a time when they are facing a severe cash crunch as a result of the coronavirus pandemic.

Under the rules of the program, though, only 10 cities and 15 counties are large enough to be able to sell directly to the Fed, according to 2018 census figures, which the Fed cites in its public guidance. That would include New York City, Los Angeles, Chicago, Houston, Phoenix, Philadelphia, San Antonio, San Diego, Dallas and San Jose.

Counties, meanwhile, must have at least 2 million people to participate, a list that includes four counties in California, three in Texas, two in New York and one in Florida, Illinois and Washington.

The local governments can still try to take advantage of the Federal Reserve’s $500 billion aid facility through their individual states. But the sheer fact they face such hurdles in the midst of an economic crisis drew sharp criticism from Democratic lawmakers.

In a letter to Fed Chair Jerome H. Powell, sent Friday evening, Sens. Chris Van Hollen (Md.), Elizabeth Warren (Mass.) and five other party leaders called on the government to rethink the program, saying it threatens to imperil “hundreds of communities nationwide.”

Lawmakers added that Congress never intended such restrictions when it adopted the $2 trillion aid package that President Trump signed into law last month. The Cares Act appropriates funds for the program targeting municipal bonds.

“There are lots of cities and counties in need that should be able to benefit from the federal program that are left out in the cold,” Van Hollen said in an interview. “Corporations have very easy access to the Fed’s credit facilities, and obviously these are cities and counties that serve a public purpose and need help now.”

The Federal Reserve and Treasury Department both declined to comment.

The scope of the economic carnage wrought by coronavirus came into sharp relief this week. More than 2,100 cities across the country — from the largest metropolitan hubs to smaller towns with just a few thousand people — said they expected major budget shortfalls due to the deadly outbreak. With scores of businesses shuttered, millions of workers unemployed and shopping and tourism facing precipitous declines, scores of cities are anticipating major reductions in tax revenue — and considering cuts to local services and layoffs to make up for the losses.

The nation’s governors have sounded a similarly bleak note: New York’s Andrew M. Cuomo (D) and Maryland’s Larry Hogan (R) said in recent days that states need about $500 billion in federal aid, or they will have no choice but to consider steep reductions in government programs at a time when local residents need help most. In Michigan, for example, the budget shortfall may be as high as $7 billion over the next 18 months, a staggering cost for the state and others like it still reeling more than a decade after the last economic downturn.

To stanch the bleeding, Congress authorized $150 billion to help city and state governments cover the costs of the coronavirus. But the aid already has proven too little, and too restrictive, local officials say, since the Trump administration has said it cannot go toward closing budget shortfalls caused by declining tax revenue. Congressional Democrats have sought to augment the fund, and give local leaders more flexibility, only to encounter steep Republican resistance.

The Fed, meanwhile, took its own steps to aid struggling local governments with a $500 billion effort to buy short-term debt at a time when the country’s roughly $4 trillion municipal bond market is in flux. The central banking system historically has been reluctant to purchase these bonds — critical to helping city and state governments fund operations and pay for infrastructure projects — out of concern it could create winners and losers.

The early reception has been mixed, as budget officials have learned more about how the process actually would work. The Fed said it would make purchases from all states, but only cities with at least 1 million people and counties with a population of 2 million. Otherwise, it said it would monitor the market to “evaluate whether additional measures are needed to support the flow of credit and liquidity to state and local governments.”

Senate Democrats, for their part, said the criteria threatened to deny “the vast majority of our country’s local governments direct access to funding, leaving them in desperate straits.” The last census pegged Baltimore at 602,000 people, for example, and Boston at 695,000. Each is facing multimillion dollar budget shortfalls, yet each remains ineligible to take advantage of the Trump administration’s new assistance, according to lawmakers.

Signing the letter was the party’s Senate leader, Charles E. Schumer (N.Y.), along with Sens. Sherrod Brown (Ohio), Tammy Baldwin (Wis.), Kyrsten Sinema (Ariz.) and Jeanne Shaheen (N.H.).

Some local governments took a more optimistic view. Under the program, states can “purchase notes of smaller cities, towns, and villages” within their borders, then take advantage of the new federal aid, said Michael Gleeson, a legislative manager for the National League of Cities. Matt Chase, the executive director of the National Association of Counties, said it would be beneficial if the Fed opened the door for more municipalities to participate but still described the program as “historic.”

Still, the restrictions could be particularly problematic in cities where African Americans live, wrote Aaron Klein and Camille Busette, top fellows at the Brookings Institution, earlier this week.

By their analysis, the U.S. government’s approach means that “none of the thirty-five most African American cities in America meets the Fed’s criteria for direct assistance.” As a result, they said, the only recourse for these cities is to “go through their state government and may be limited by that state’s ability to access funds compounded by the state politics.”

To that end, Democrats on Friday called on the Trump administration to expand the program. “Without quick access to federal assistance,” they wrote, “these governments will be forced to cut services or raise taxes — both of which can harm public health and the economy when they are most vulnerable.