Undated (AP) _ California and Maine got their state budgets signed at last, raising taxes in both states and sending Maine employees back to work. In Illinois, leaders announced a tentative settlement to their budget woes.

Elsewhere it was budget impasse as usual.

Minutes before midnight Tuesday and 16 days into a new fiscal year, California's state government received the authority to spend money again when Gov. Pete Wilson signed a $55 billion budget bill.

''It was a difficult budget, which understates it by a lot - one of unprecedented challenge, but I think under the circumstances a fair and wise budget,'' said the Republican Wilson.

Wilson also signed a $2.3 billion tax bill, the last piece in a package of tax increases and cuts needed to erase a $14.3 billion deficit, and workers' compensation restrictions the governor demanded as part of the budget deal.

Tuesday was the deadline for Wilson to sign or veto the budget or to allow it to pass into law without his signature. He made $191 million in spending reductions before signing the measure.

The tax bill, which includes higher income taxes for the wealthiest Californians, and the workers compensation legislation both passed the Legislature Tuesday.

The workers' compensation measure restricts stress-related claims during the first six months of employment. Wilson wanted the reductions to offset the impact of higher taxes on California's business and job market.

He had already signed $5 billion in new sales, alcohol and motor vehicle tax hikes and enacted more than $7 billion in cuts in welfare, health benefits, education and other state programs.

Lack of a budget held up paychecks for 6,843 state workers and delayed refund checks for 5,657 taxpayers.

Early today Maine Gov. John R. McKernan, a Republican, signed a $3.2 billion state budget and put state government fully back in business for the first time in more than two weeks. The Legislature passed the budget Tuesday.

The two-year spending plan authorizing $300 million in new taxes, returns to work 10,000 state employees idled all but three working days since July 1.

McKernan relented on his vow not to sign until he got a workers' compensation bill that substantially cut what businesses pay for the mandatory insurance program.

He said part of such an overhaul could be passed today. But major issues still unresolved - including which injuries can be covered and duration of benefits - will be voted on at a special session next month.

In Illinois, the light at the end of the tunnel appeared today when Gov. Jim Edgar said that he and legislative leaders have reached a tentative agreement to end the state's budget impasse. Some 10,000 state workers had gone without paychecks Monday and thousands more were threatened with the same fate later in the week.

But battling continued in Connecticut, where Gov. Lowell P. Weicker Jr. on Tuesday made a prime-time televised speech, criticizing the Legislature and asking the public to give his income tax plan a 2 1/2 -year tryout.

''The choice then is between what works and what feels good - between an honest budget and another fraud,'' a combative Weicker.

Weicker offered what he called a fair compromise - if the Legislature reverses itself and accepts his proposal for a state income tax, the levy will automatically expire on Dec. 31, 1993, unless 60 percent of the Legislature votes to keep it.

Senate President Pro Tem John Larson and other legislative leaders from both parties said Weicker's speech would not slow their drive to override his veto and put into place a no-income tax budget.

Tuesday was the start of a furlough program requiring the 100,000 Georgia state workers to take off one day a month without pay. The move was ordered last week by Gov. Zell Miller, who also froze hiring, travel and new programs.

Miller has said the furloughs may last two months, until he can offer the Legislature plans for cutting up to $400 million from the current budget.

Pennsylvania, too, is functioning without full spending authority and with neither a spending plan nor a tax package are in sight.

But in Pittsburgh, they've begun an effort to avoid layoffs and shrink a potential $15 million deficit by collecting on long overdue sewer and property tax bills.

Tax collectors will mail 18,142 lien notices next week to property owners who owe the city $11.7 million. The bills date as far back as 1988.

''It's the smart bomb of tax collection,'' said Ben Hallyar, Pittsburgh finance director. ''Before you lay off a single person, you want to make sure that every delinquent tax dollar has been collected.''

Maryland's highest court today upheld an earlier court decision that backed the governor's authority to impose a longer work week on state workers.

Gov. William Donald Schaefer's had issued an executive order earlier this year for nearly 40,000 state employees increase their workweek from 35 to 40 hours. The executive order is expected to help ease a $200 million state budget deficit for fiscal 1992.