An influential New Hampshire lawmaker thinks legalized gaming can be passed by June, opening the possibility that the dice will be rolling in the Granite State before Massachusetts gets its first casino open.

New Hampshire state Sen. Lou D’Allesandro said he’s “cautiously optimistic” that a bipartisan plan to license one casino will pass before the Legislature’s June recess.

“I would hope we could expedite the process and get this legislation passed and move this forward,” D’Allesandro told the Herald last night. “We’ve got to have it done by June. Hopefully, we’ll get it done sooner than that so we can begin the process. The sooner the better.”

Past attempts to legalize gaming in New Hampshire have failed, but now Gov. Maggie Hassan is making a strong push for one “high-end” casino, likely at Rockingham Park in Salem, to thwart Massachusetts from siphoning off gambling cash. Hassan included $80 million in her two-year budget from casino licensing fees in a move to turn up the heat on the Legislature.

“The question is, will we allow Massachusetts to take revenue from New Hampshire’s residents to fund its needs, or will we develop our own plan that will allow us to address social costs and invest in our priorities?” Hassan said this week.

The Massachusetts Gaming Commission is slated to issue a slots license this fall and two of the state’s three casino licenses by February 2014. Gaming experts said less red tape in the Granite State could result in a casino opening there first.