Lawmakers got down to the business of working out the differences between House and Senate plans to fund the state’s ongoing shelter and migrant crisis, and their first order of business was to close the public out of their deliberations.

Members of the joint committee appointed to match the Senate’s $863 million plan to House’s $245 million proposal met at the State House on Monday, when the committee’s leaders both expressed their understanding of the need for haste.

“I look forward to working with all of you to get this rectified as quickly as possible. You and I are experienced at it,” Senate Ways and Means Chairman Michael Rodrigues said told his House counterpart. “So I’m sure we will accomplish that goal quickly.”

“I’m looking forward to working with you, and all of you, on this supplemental budget bill trying to get it done as quickly as possible. We have some obviously important pieces in there that are of immediate need. And I know we share a desire to see this get to the governor’s desk as soon as we can,” House Ways and Means Chair Aaron Michlewitz said.

As is usually the case on Beacon Hill, the joint committee’s first and only public activity was to move into private executive session.

The state’s Emergency Assistance shelter system has been full for months, pushed to maximum occupancy by an influx of foreign migrant families. Massachusetts is alone among the 50 states in guaranteeing a right to shelter for pregnant women and parents of small children.

With more than 7,500 families currently occupying shelter space and hundreds more at overflow sites waiting for a spot, state officials have estimated that the funds to continue housing that many people will run dry sometime this spring.

Gov. Maura Healey, who declared a state of emergency around the migrant influx last August and filed the original request for a $282 million supplemental budget in January, said she supports the work of the joint committee, but wouldn’t speak to the pair of bills they are working to reconcile until she sees a final product.

“It’s up to the Legislature now,” she said.