(Reuters) - Partial government shutdowns in Maine and New Jersey stretched to a second day on Sunday as lawmakers returned to their respective state capitals in a bid to break budget impasses that have led to the suspension of many nonessential services. In Maine, a bipartisan budget committee met in Augusta in hopes of breaking a stalemate between Republican Governor Paul LePage and Democratic lawmakers. The shutdown came after LePage threatened to veto a compromise reached by lawmakers in the state’s $7.055 billion, two-year budget. At New Jersey’s statehouse in Trenton, there was little evidence of progress in resolving a fight over a health insurance bill that Republican Governor Chris Christie said must be passed alongside the state’s budget.  Maine state police, parks and all offices responsible for collecting revenue planned to operate during the shutdown, the state’s first since 1991, but the majority of 12,000 state employees will be furloughed. New Jersey residents were not so lucky. With the July 4 holiday weekend in full swing, the shutdown there included the closure of Island State Beach Park, one of New Jersey’s few free public beaches, and all other state parks.  Although he beach park was closed to the public, Christie took a state helicopter on Saturday to a gubernatorial residence there to be with family and said he would go back on Sunday night.  “That’s just the way it goes. Run for governor, and you have can have a residence there,” he said when pressed on the issue.  At a news conference on Sunday afternoon, the governor said he had not spoken since Friday to Democratic holdouts.  The impasse could mean a furlough for 30,000 to 35,000 state employees on Monday. In Maine, the stalled budget proposal would have repealed a measure voters approved in November for a 3 percent income tax hike on residents earning more than $200,000 a year. It also contained a 1.5 percent increase in the lodging tax, while increasing funding for public education by $162 million. LePage has promised to veto any spending plan that raises taxes. A six-member bipartisan House-Senate budget panel huddled into the evening on Sunday seeking to reach a deal that would win the two-thirds vote needed for passage of an emergency budget bill in both legislative chambers. Mary-Erin Casale, a spokeswoman for Democratic House Speaker Sara Gideon, said a new compromise could be ready for a vote as early as Monday morning, about the time state employees planned to protest the shutdown at the capitol. A spokeswoman for the governor could not be reached for comment on Sunday. At the center of New Jersey’s stalemate was a plan by Christie to shake up the state’s largest health insurer, Horizon Blue Cross Blue Shield, which he said lacked sufficient transparency and spent too much on salaries.  He threatened to cut $150 million in school funding and other items unless lawmakers adopt his proposal, which would redirect some of Horizon’s reserves to drug addiction treatment and other services. Christie offered to hear Democrats’ proposals for breaking the impasse, saying: “It should end today,” but acknowledged a settlement was unlikely so soon. Christie, a former presidential contender whose reputation was tarnished by the Bridgegate traffic scandal involving some of his closest aides, ranks as the least popular governor in state history. He is in his second and final term. Assembly Speaker Vincent Prieto and other Democrats have criticized the Horizon bill as “bad public policy,” insisting that it be considered after the budget is passed. Christie blamed Prieto for the shutdown and vowed on Sunday to stand by the Horizon bill, saying: “I got elected by a lot more people than Vinnie Prieto did.” 