Broadway theaters, which have been closed since March, applauded the relief package.

“We are grateful for this bipartisan agreement which will provide immediate relief across our industry and a lifeline to the future,” Charlotte St. Martin, the president of the Broadway League, the trade organization for producers and theater owners, said in a statement.

Nataki Garrett, the artistic director for Oregon Shakespeare Festival, said that the aid would be crucial for nonprofit theaters. “Our situation was critical and dire,” she said.

But the leaders of some large nonprofit cultural organizations worried that the way the bill is structured — giving priority to organizations that lost very high percentages of their revenue before considering the rest — could put them at the back of the line for grants, since they typically get a significant portion of revenues through donations.

With the bill set to be approved in both chambers of Congress as early as Monday evening, arts groups around the nation were cautiously celebrating while studying the fine print to see what kind of aid they might qualify for. Most doubt the entertainment industry can fully swing back into action until well into next year, at the earliest.