The Reagan administration, in its first big bill to taxpayers for the current recession, has notified Congress that it needs at least $1.1 billion in additional funds for unemployment insurance payments to the states.

The $1.1 billion is in addition to $2.3 billion appropriated in December to help states that have exhausted unemployment benefit funds because of high jobless rates. That was to have lasted through March 31.

The "emergency," as the Office of Management and Budget labeled it in formal notification to Congress earlier this month, stems from the fact that unemployment is higher than anticipated in last summer's updated budget projections.

The forecast, upon which appropriations were based, was for a jobless rate of 7.7 percent for the last quarter of 1981 and 7.3 percent for 1982. Last month's unemployment rate was 8.9 percent and this month's rate is expected to be higher.

The notification, which will be followed by a request for a supplemental appropriation in President Reagan's budget proposal to Congress next month, has already provided fodder for Democratic cannons. It was cited by House Majority Leader James C. Wright Jr. (D-Tex.) in criticizing Reagan's State of the Union address on Tuesday night.

"Optimism is good, and I'm glad the president exudes it," Wright said. But "realism also is necessary" to combat rising unemployment, high interest rates and big deficits, he added.

Because unemployment benefits are mandated by law and take the form of a political imperative during a recession, Congress is expected to approve the extra money.

But the debate could trigger a push for more unemployment assistance, which the administration may not want, and for a revised budget resolution that would have to acknowledge a likely 1982 federal deficit of about $100 billion, which sends shudders through Congress.

To appropriate more for unemployment benefits, Congress would have to waive its budget ceiling or approve a new budget resolution for 1982, and Wright said yesterday that, in conjunction with the budget debate, he and other Democrats may push to restore funds cut from employment services last month under administration pressure.

According to Wright, cuts approved in connection with the December continuing resolution for funding the government through March 31 resulted in layoffs of about half the staffs of local employment service offices, or 13,000 to 15,000 people.

He said 800 to 1,000 employment offices have been closed.

"It's extremely painful because this is coming as unemployment is going up," said Wright, noting that the employment service offices placed about 3 million people in jobs last year.

It was not clear yesterday how much in extra money the administration may actually request or what the strategy of congressional Democrats will be. House Democratic leaders are planning to meet today with the chairman and subcommittee chairmen of the Appropriations Committee on strategy.

One Democratic source said the supplemental appropriation could be considerably more than $1.1 billion--perhaps $2 billion or more--if it contains enough money to last through the end of the fiscal year on Sept. 30.

While this would add to the deficit for fiscal 1982, an administration official said the extra money has already been included in revised deficit estimates for the year, which will appear in the 1983 budget that Reagan submits to Congress next month.