The Federal Reserve could soon expand its plans to buy municipal bonds, as lawmakers from both parties pressure the central bank to do more to support smaller cities and counties suffering amid fallout from the coronavirus.

Fed officials said on April 9 that they would begin purchasing municipal bonds using their emergency lending powers, pledging to buy up to $500 billion in bonds from states and the biggest cities and counties. In doing so, they crossed a line they have long treated as sacred: buying local bonds is potentially charged territory for the politically independent Fed.

While the central bank has yet to announce a start date for the new program, its plans have been met with both hope and criticism. New Jersey is already preparing to tap the program. Lawmakers and analysts have been blasting the program for not going far enough. It is open only to states, counties with populations of more than two million, and cities of one million or more.

The Fed made it clear from the outset that it could push the program further, saying in a statement on April 9 that it would continue monitoring markets and would “evaluate whether additional measures are needed to support the flow of credit and liquidity to state and local governments.” Its chair, Jerome H. Powell, reiterated that message on Monday, telling a Democratic lawmaker that the central bank was looking at how it could make the program broader.

Mr. Powell “assured” Senator Chuck Schumer of New York, the Democratic leader, that the Fed was “working to make the program directly accessible to more cities and counties,” Mr. Schumer said in a statement.

That is in line with other Fed officials’ statements. Central bank regional presidents, who do not vote on the Fed’s emergency lending programs but who do weigh in on them, have hinted that the program could become further reaching.

“The first pass is really a first pass — it shouldn’t be viewed as a final word on any of these things,” Raphael Bostic, the president of the Federal Reserve Bank of Atlanta, said on Thursday in a call with reporters. “The distribution of funds across communities is something that we definitely are worried about.”

The Fed has spent decades treating municipal bond buying as a bright line that should not be crossed. Purchasing state and local debt amounts to bankrolling local political decisions, a move that could open officials up to criticism if the money were deployed badly.

But as the coronavirus plunges the economy into a steep downturn, causing growth to swan dive in a way unseen since the Great Depression, Mr. Powell and his colleagues have been breaking all of their own rules — taking a “move fast and save the economy” approach, despite the consequences that might follow.

Congress specifically directed the central bank in the CARES Act response package to try to help out state and local governments. The Fed complied weeks later, and its initial, hastily formed pass at the municipal bond market relied on simplistic cutoffs: Officials pledged to buy from counties with more than two million people or cities with more than one million, and from states.

That left out heavily black cities like Atlanta and Baltimore, based on a Brookings Institution analysis, and touched off prompt criticism.

“Congress made no distinction regarding the size of a municipality that should directly benefit from such a program,” Representative Maxine Waters, Democrat of California and the chairwoman of the Financial Services Committee, wrote in a letter on April 16 poking holes in the program’s design.

Other lawmakers have followed her in calling for more. Democratic senators including Elizabeth Warren of Massachusetts and Mr. Schumer sent a letter to Mr. Powell on Saturday “expressing serious concern with the arbitrary population thresholds used to determine eligibility.”

Senator Michael D. Crapo, Republican of Idaho, the chairman of the Senate Banking Committee and one of Mr. Powell’s key bosses, pointed out in a letter that as it stands now, “no city or county in Idaho would qualify, which precludes rural communities from receiving significant and critical assistance.”

Such concerns will probably draw a response before long, Ian Katz, an analyst at Capital Alpha, wrote in a note on Sunday.

“The complaints about the reach of the Municipal Liquidity Facility seem like common sense and probably won’t be ignored,” he wrote. That said, the outpouring of questions “may end up vindicating those at the central bank who view this as fiscal policy that Congress should decide.”