The Central Florida families affected by Saturday’s FEMA deadline were scattered across town, many of them in the motels that line Route 192, a long drag of fast-food joints, souvenir shops and gas stations en route to Disney World. Just off the same highway is the purple Magic Castle Inn, the setting for “The Florida Project” — a movie about, yes, a family living in a motel.

The Super 8, nestled between a coin laundry and an IHOP, has become the community’s focal point. Its open layout lends itself to socializing, and a common room in the lobby, outfitted with a few tables and a coffee machine, brings guests together in the mornings for breakfast and in the evenings to chat.

Television news crews regularly come by for interviews. Politicians frequently drop in. Representative Darren Soto, an Orlando Democrat who was the first Puerto Rican elected to Congress from Florida, visited Friday evening. One of his aides held office hours at the motel on Saturday, as a World Cup match between Uruguay and Portugal played in the background.

By then, it had become clear that FEMA, which has extended the temporary shelter assistance three times, would not offer any such relief, despite pleas from Mr. Soto and other Democrats, including Senator Bill Nelson of Florida. Mr. Nelson urged FEMA to activate a separate disaster housing assistance program to provide rent subsidies to families, as the agency did after Hurricane Katrina until 2009.

Lenisha Smith, a FEMA spokeswoman, said there was “no need” for that aid because another program, called direct lease assistance, provides similar services “without the additional complexities and red tape.” However, critics like Christiaan Perez, a spokesman for LatinoJustice PRLDEF, say direct lease is too narrow to benefit most of the needy Puerto Rican families.

The group sued Saturday in federal court in Massachusetts, which has the highest population of families receiving temporary sheltering assistance after Florida and Puerto Rico. Federal District Judge Leo T. Sorokin issued a limited temporary restraining order in the case late Saturday.