The 150-year-old Taunton State Hospital, which was on Governor Deval Patrick’s chopping block, got a reprieve Thursday as lawmakers voted to override his veto and keep the psychiatric hospital open.

The state Senate rejected Patrick’s budget veto to close the hospital in Southeastern Massachusetts. The House of Representatives overrode the veto Wednesday.

Senators also shot down the governor’s proposals on restrictions for welfare purchases and requiring proof of state residency when registering a vehicle. The House also rejected the two proposals the previous day.

With the override, lawmakers ensured that $5.1 million to support 45 beds at the hospital will remain in the new state budget. The funding was ­included as a compromise ­between the House and Senate budget proposals.

Since January, the fate of the hospital has been in limbo, as the Patrick administration announced it was closing Taunton State Hospital, saying it was ­antiquated and not cost-effective. He and House leaders suggested moving most of the hospital’s patients to a new state hospital opening in Worcester.

As a compromise, Senator Marc Pacheco, a Taunton Democrat, pushed to keep the hospital open with 72 beds and to study the state’s mental health system. ‘‘I’m very pleased with both vetoes and the language for an independent study,’’ Pacheco said Thursday. ‘‘It’s a clear message from the Legislature that the budget is about more than [money].’’

Senators struck down the governor’s proposal to cut the list of businesses that would not be allowed to accept cash assistance purchases, saying the amendment would weaken the Legislature’s budget proposal. Patrick’s proposal would still ­allow the cards to be used at nail salons and jewelry stores, points of purchase lawmakers wanted to eliminate.

Patrick told reporters Thursday that while he shares the concerns of lawmakers when it comes to protecting the integrity of the state’s welfare system, his proposal would have created a practical way to combat fraud. He said he also was concerned with some of the ­‘‘demeaning’’ comments made during the Legislature’s debate.

‘‘It’s one thing to talk about how we assure that these programs are used to their intended purposes, but it’s not necessary for us to go the extra step to make it seem like there is fault associated with being poor,’’ he said.

The governor also defended his vehicle registration amendment, saying it would not go against public safety. He amended a state budget provision requiring anyone seeking to register a car in Massachusetts to provide proof of legal US residency, which immigration advocacy groups oppose. The governor is calling for simply requiring vehicle owners to prove state residency.

The residency language is part of a broader measure that would allow applicants for ­motor vehicle or trailer registration to present a driver’s ­license, identification card or Social Security number to the Registry of Motor Vehicles as proof of ID. It would also allow the Registry to grant exemptions for out-of-state college students, military personnel, ­elderly residents and disabled people. Advocates for immigrants had urged Patrick to veto the provision attached to the fiscal 2013 budget.