NEW YORK — Stocks fell about 3% on Wall Street Monday as Congress hit another roadblock in talks to inject nearly $2 trillion into the economy. Even an extraordinary flood of support from the Federal Reserve wasn’t enough to lift stocks, as frustration with Washington rises along with the number of coronavirus cases.

Another attempt to advance the aid bill on Capitol Hill failed in an afternoon vote. The plan would send checks to U.S. households and offer support for small businesses and the hard-hit travel industry, among other things, but Democrats say it too heavily favors corporations at the expense of public health and workers.

As Congress was locked in stalemate, the number of known infections worldwide jumped past 350,000. After just a few weeks, the United States has more than 35,000 cases and more than 400 deaths.

“The Fed is only important to the extent that it keeps the markets running smoothly,” said Chris Zaccarelli, chief investment officer for Independent Advisor Alliance. “It’s completely up to the federal government, and I mean Congress and the executive branch, at this point.”

With Monday’s losses, the stock market has lost more than a third of its value since its record last month, as more businesses shut down in hopes of slowing the spread of the coronavirus. Economists increasingly say a recession seems inevitable, analysts are slashing their forecasts for upcoming corporate profits and no one can say for sure how deep the downturn will be or how long it will last.

Markets are likely to remain incredibly volatile as long as the number of new infections accelerates. Until then, investors are looking for both central banks and governments to do their parts to support the economy.

The Fed came through Monday, saying it would buy as many Treasurys and mortgage-backed securities as it takes to get lending markets working smoothly again. It goes way beyond the $700 billion in purchases announced last week, which economists called a “bazooka” of support.

It also said it will buy a wide range of investments, including corporate bonds for the first time, to improve trading in markets that help home buyers purchase houses, state and local governments borrow and businesses to get enough short-term cash to make payroll.

“This is excellent, comprehensive, covering many areas of the financial markets, their function, the flow of credit — this is exactly what was needed,’’ said Donald Kohn, former Fed vice chair and now senior fellow at the Brookings Institution. “The Fed has hit it out of the park as far as I’m concerned.’’

“The key issue now is getting the fiscal response straight,’’ said Kohn, saying that Congress needs to finance a stabilization fund to back up the Fed’s efforts.

On that point, Congress debated through the weekend on the rescue plan, but top White House officials and congressional leaders are struggling to finalize it. Democrats blocked a vote to advance the package Monday, trying to steer more of the assistance to public health and workers.

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