State Democrats tentatively agreed last night to try to save about $4 billion in social programs from President Reagan's budget ax when the Senate begins work today on the administration's proposed spending cuts.

But the Democrats are outnumbered, and sharp differences were expressed on many issues in their two days of closed-door caucuses on the budget cuts, raising doubts about how unified the Democratic minority will be in the voting.

Their effort to frame an alternative came as the president walked away with an easy early victory in the Senate, where his proposal to skip an April 1 increase in milk price supports was approved as expected and sent to the House, 88 to 5.

The House also cast a frugality vote, as it cut $3.3 million from its own budget for next year. But Reagan's tax cut proposals continued to run into trouble. House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) warned they cannot pass in their present form, and urged Republicans to help write an alternative. [Details on Page B1.]

The Senate Democrats' plan may be changed when they meet again this morning to finish work, according to participants. As of last night, Senate sources said, the Democrats had agreed to push for restoration of the following:

$200 million for economic development assistance, $100 million for legal services for the poor, $100 million for Conrail, $300 million for job training, $300 million for veterans' health services, $300 million for food stamps and $300 million for school lunches.

Also, $300 million for low-income energy assistance, $190 million for health services, $890 million for education, $800 million to restore the minimum Social Security payment and $50 million for urban development grants.

While declining to discuss details of their work, Senate leaders said the proposals will be offered as separate amendments rather than a comprehensive package, apparently out of fear they might lose everything on a straight up-or-down, one-shot vote.

Democratic Whip Alan Cranston (Calif.) said some proposals may be supported by as many as 95 percent of the Democrats, while others may attract only 30 or 40 percent.

As the Democrats caucused, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) said the Republicans were in "pretty good shape" to withstand anything the Democrats could throw at them, including parliamentary maneuvers to derail the spending cut proposal.

The measure before the Senate today marks the first step in congressional action on Reagan's overall economic program: instructions to congressional committees to cut programs within their jurisdiction by the $36.4 billion arrived at last week by the Budget Committee. The committee endorsed most of Reagan's cuts and added some of its own.

At the House Budget Committee, Alice M. Rivlin, director of the Congressional Budget Office, came under fire from Republicans for an analysis concluding that the administration has underestimated the deficits that will be created by its economic program.

In a report to Congress, CBO was less optimistic than the administration about the Reagan program's impact on inflation, interest rates, economic growth and unemployment and concluded that the fiscal 1982 deficit will reach $67 billion, or $22 billion more than the administration forecasts. It also predicted the administration will fall $49 billion short of its goal of a balanced budget for 1984.

Rivlin described Reagan's set of economic assumptions as "very optimistic but not impossible," saying CBO leaned toward the pessimistic side because of "historic experience" indicating that presidents, regardless of party, tend to be too optimistic about success of their programs.

Rep. Ed Bethune (R-Ark.) accused CBO of "biases against what the president is trying to do" and several other Republicans joined in asserting that CBO was wedded to liberal economic theories Reagan had rejected in developing his program.

Apparently assuming the likelihood of such a challenge to the CBO's numbers, Budget Committee Chairman James R. Jones (D-Okla.) opened the hearing with a defense of CBO's analysis.

Referring to Reagan's criticism of an earlier CBO prediction of bigger deficits than the administration foresees, Jones said, "This CBO report is not 'phony' or 'cynical.' It is a best judgment, realistic, nonpartisian, expert analysis."

Jones said "careful attention" had to be paid to Rivlin's analysis, but after the hearings he declined to say whether the Budget Committee, in preparing budget targets for 1982, would adopt CBO's economic assumptions.

He said, however, it appears unlikely Congress will be able to get the 1982 deficit under Reagan's figure of $45 billion. Jones had said earlier he hoped the deficit could be kept to about $30 billion. "But I don't know if we can get there from here," he said after the hearing.

The House cast a modest vote for frugality as it approved $39.6 million to operate its committees and its computerized information system for 1981. Pushed by Republicans, Democratic leaders proposed and the House approved, 407 to 2, a $3.3 million cut in the amount recommended by the House administration committee.

This was about $365,000 less than spend last year, but about half the cut was taken from the computer system and most committees will have more than they spent last year.

A Republican attempt to make a 10 percent cut below last year's actual spending which would have amounted to twice that actually voted was rejected by a straight party-line vote. Democrats, who still control the House though not the Senate said these funds are needed to oversee adequately actions of the Reagan administration.