THE BIG 3 on Beacon Hill met via Zoom on Thursday morning with the state’s representatives in Congress, enlisting their help in seeking federal dollars and regulatory changes to help ease the shelter crisis in Massachusetts.

Sounding more and more like officials from border states who complain about bearing the burden of immigration, the Massachusetts officials are urging the federal officials to press the Biden administration to speed up work authorizations for migrants and provide more money for financing the shelter system.

“We stressed to them that we need help,” said House Speaker Ron Mariano, who disclosed the meeting with the congressional delegation at a State House press conference dealing with a different matter. “Unless we get help, we’re going to have some difficulties,” he added.

Gov. Maura Healey’s office confirmed the meeting but didn’t publicize it. The governor’s spokeswoman declined to characterize the response of the federal lawmakers.

Senate President Karen Spilka issued a general statement.  “The reality is that we are doing all we can to help the desperate families who are arriving here in ever increasing numbers, but we absolutely need help from our federal partners to marshal the resources required to house these parents and children and help them get on their feet,” she said.

Mariano said the biggest headache is having no control over the situation. Healey has requested an additional $250 million in a supplemental budget to address the influx of migrants, but Mariano isn’t sure that’s enough.

“The money that we’re talking about in the supp is just the beginning. We have no idea what the total bill is going to be,” he said.

He said the number of migrants coming to Massachusetts is difficult to forecast. “The frustration is the numbers change dramatically daily,” he said. “The hope is — and it’s only a prayer — is that cold weather slows the flow of families coming across the border.”