AUGUSTA — A week after a budget-balancing bill fell short of passage, the Maine Senate moved quickly Thursday to pass a measure that would close a $120 million revenue gap while cutting Medicaid coverage for thousands of Mainers.

The Senate’s 27-8 vote sent the measure to Gov. Paul LePage. The House last week gave the budget rewrite the needed two-thirds majority approval it needs in order to take effect immediately.

Without saying whether he will sign the budget, which covers a period through June 30, LePage said he was pleased to hear it passed.

“The fiscal integrity of our state is frail, but the passage of this bill today is a step in the right direction,” LePage said in a statement.

The governor had called for deeper cuts in MaineCare, the state’s Medicaid program for the poor and disabled, than the final budget adjustment provides, saying the state would run out of money to pay for services if cuts aren’t made soon. The program cost more than $552 million in state funds in fiscal 2011.

Thursday’s Senate approval followed a deal over a veterans’ benefits issue following Democrats’ defeat of the bill last week. In negotiations during the last few days, Democrats asked for language in the budget that would have helped transition veterans currently on MaineCare to other benefits such as those provided by the Veterans Administration.

Majority Republican leadership rejected the Democrats’ idea, but LePage and GOP leaders gave assurances that the Democrats’ proposal will be made a priority this session, but handled separately from the budget rewrite bill, Senate Democratic leaders said.

“Simply, Democrats wanted to create a softer landing for the people of Maine transitioning off of MaineCare,” said Senate Democratic Leader Barry Hobbins of Saco.

The budget package, hammered out over weeks of public hearings and deliberations by the Appropriations Committee, reduces the income threshold for parents of children on MaineCare to 133 percent of the poverty level, or $30,657 for a family of four, cutting their ranks by 14,000; trims optional services such as chiropractic and dental care for MaineCare recipients; and limits drug choices for MaineCare recipients.

It also caps enrollment of childless adults in MaineCare by freezing enrollment and through attrition.

House Speaker Robert Nutting said the budget corrects many of the structural problems that have led to repeated financial shortfalls within the Department of Health and Human Services. He said the shortfalls were the result of “unsustainable, skyrocketing enrollment in MaineCare” over the past decade.

Nutting, R-Oakland, also noted that tough budget work lies ahead. Lawmakers must now make around $84 million in proposed cuts to DHHS for fiscal 2013, which begins July 1.

The House Democratic leader, Rep. Emily Cain of Orono, said she was relieved the budget didn’t take health care coverage away from 65,000 people as the governor’s initial budget proposal would have done.

During a brief debate before Thursday’s vote, Sen. Richard Rosen of Bucksport, the Republican who chairs the Appropriations Committee, called the budget “a consensus document” and “the product of considerable effort and work.”

“Like any consensus document, it has imperfections,” said Rosen.