Reports of more planeloads of asylum-seeking migrants en route north from Texas courtesy of Governor DeSantis of Florida, this time to President Biden’s home state of Delaware, had state officials there scrambling on Tuesday to accommodate the newcomers.

By late Tuesday, however, the flight that was said to be arriving at an airport near Rehoboth Beach, Delaware, where Biden often spends his weekends, from San Antonio had not arrived.

Earlier in the day, the White House press secretary, Karine Jean Pierre, said Biden administration officials were aware of reports about the flight and preparing for it.

“We are coordinating closely with state officials and local service providers who are prepared to welcome these families in an orderly manner as they pursue their asylum claims,” Ms. Jean Pierre told reporters at the White House.

Last week, Mr. DeSantis spent $615,000 of Florida taxpayers’ money to fly two planeloads of Venezuelans who had reached Texas from San Antonio to the exclusive island enclave of Martha’s Vineyard off the coast of Massachusetts. After an initial warm welcome from residents of the island, the migrants were relocated to a National Guard base at Cape Cod.

Many of the migrants later said they were misled about their destination and what was awaiting them on the island, prompting calls from some Democratic officials for criminal investigations into the flights. A group of them filed a class-action lawsuit against Florida officials Tuesday, claiming they were used as “pawns in a political stunt.”

The sheriff of Bexar County, Texas, Javier Salazar — where the flights originated — said Monday that he was initiating such an inquiry, but could not say what laws he thinks were broken. Officials in Massachusetts, including the state’s attorney general and a U.S. attorney in Boston, also have said they are looking into the matter. 

Migrants arriving at the border who are seeking asylum are routinely processed by immigration authorities and then released pending the outcome of legal proceedings. As asylum seekers, they are legally allowed to work and live anywhere in the country until their cases are settled, which can take years.

The border patrol announced Monday that so far in fiscal year 2022, which ends September 30, more than 2 million migrants have arrived at the southern border, many of them seeking asylum. The figure is an all-time high, and reflects record numbers of migrants fleeing communist regimes in Cuba, Nicaragua, and Venezuela.

Democrats decried the Martha’s Vineyard flights as a political stunt, but if the intention was to bring attention to the growing crisis at the border, the move was successful. Since last week, a crisis that had been all but ignored by much of the national media is back on the evening news and the front pages of major newspapers.

NBC News reported Tuesday that Mr. Biden’s Department of Homeland Security is prepping plans to begin transporting some of the migrants massed in cities along the U.S.-Mexico border to cities away from the border, beginning with Los Angeles.

Officials in the department are said to be jokingly calling the plan the “Abbot Plan” after the Republican governor of Texas, Greg Abbott, who began busing migrants to Democrat-led cities such as New York, Chicago, and Washington, D.C., months ago.

The flights to Massachusetts cost taxpayers in Florida $615,000, according to local press reports, money that came out of the state’s general fund and was authorized by the state legislature as part of a $12 million program to relocate unauthorized immigrants. 

Mr. DeSantis’s lieutenant governor, Jeanette Nunez, last month warned the country that Delaware might be next on the list of states and cities targeted.

In a radio interview on Spanish-language WURN in late August, Ms. Nuñez said the Biden administration’s border policies are affecting not just states on the border and that Florida would act in the best interests of its residents and communities.

“The state doesn’t have jurisdiction over immigration, but we do have jurisdiction over the well-being of our residents and our communities,” Ms. Nuñez said. “That’s why the governor has worked with the legislature to secure funding to try and assure that those people who come here illegally … we are going to — quite frankly — send them to the state of Delaware.”