Gov. Maura Healey said a five-person team sent to the southern border to “educate” people there about the lack of shelter availability for migrants in Massachusetts had a “successful” trip just as they were scheduled to return later Wednesday.

Healey’s first term in office has been marked by a maxed-out state-funded shelter system struggling to keep up with the number of families arriving in the Bay State from other countries. She sent members of her administration south to make “connections” with immigration officials, non-governmental organizations, and families at the Texas-Mexico border.

Healey, who said she has not talked to Texas Gov. Greg Abbott, said Massachusetts has been dealing with a migrant crisis “for a long time now” and a team was sent to “be clear with our message that we have reached capacity here.”

“We don’t have housing available right now, and we wanted to be really clear. It’s something I’ve been saying for a long time, but I think it was important that we be able to communicate directly with folks on the ground,” she told reporters at the State House. “I think it’s successful. I think it’s important that we be out there with that message.”

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The group arrived in Texas Sunday and was scheduled to visit sites in San Antonio, McAllen, Hidalgo, and Brownsville, the most common points of entry for families that later arrive in Massachusetts, according to the Healey administration.

The trip comes months after the Healey administration put a 7,500-family limit on the state-run shelter system and forced those who were waiting for placement to seek temporary housing in overflow shelters.

Beacon Hill also placed a nine-month limit on families’ time in shelter and those at overflow sites must reapply for benefits every 30 days.

Non-stop demand on the system has resulted in a massive price tag, with officials estimating the state could spend $932 million on the emergency shelter system this fiscal year and $915 in the next.

MassGOP Chair Amy Carnevale criticized the Texas trip, calling it a “publicity stunt that will neither address the migrant crisis in Massachusetts nor reduce the influx of migrants entering the commonwealth.”

“They can engage in rhetoric and publicity stunts all they want, but without concrete steps to limit access to emergency housing, nothing will change. To stop incentivizing migrants from coming to the commonwealth, the right to shelter law must be amended to restrict program access based on the duration of residency in the commonwealth,” she said in a statement.