President Reagan's tax-cut program survived its first major congressional assault of the year last night as the Republican-controlled Senate handily defeated two Democratic-led attempts to defer or repeal the 10 percent individual income tax cut scheduled for July, 1983.

The Reagan victory came as the Senate, brushing aside repeated Democratic attempts to restore funds for social welfare programs, struggled to wrap up its version of the budget for the 1983 fiscal year that starts Oct. 1.

But Republican leaders' control broke down shortly before midnight when the Senate indicated on a 58-to-41 vote its intention to approve $1.7 billion for railroad retirement benefits by 1985, prompting Majority Leader Howard H. Baker Jr. (R-Tenn.) to end debate for the night. The Senate hopes to finish work on the budget today.

In the earlier debate, Republicans generally held fast behind Reagan's tax-cut program and were joined by as many as 17 Democrats, some of whom are up for reelection this fall, in reaffirming their support for the huge, controversial tax cuts that Congress approved last year at Reagan's behest.

In the first test of Reagan's tax program this year in either house of Congress, the Senate voted, 68 to 32, against a proposal by Sen. Ernest F. Hollings (D-S.C.), ranking Democrat on the Senate Budget Committee, to repeal the 1983 tax cut atop $107.2 billion in tax increases that the Senate Budget Committee has proposed for the next three years.

Then it voted, 63 to 35, against a proposal by Senate Minority Leader Robert C. Byrd (D-W.Va.) to put the Senate on record as favoring deferral or drastic alteration of the tax cut as part of committee's $107.2 billion package of tax increases through 1985.

Hollings' proposal would have added $76.3 billion in taxes over the next three years, for an overall total of $183.5 billion, while reducing projected deficits by the same amount and bringing the budget to within striking distance, $28.5 billion, of balance by 1985.

Byrd's proposal would have relieved pressure for other tax increases but would not have reduced the deficit beyond what the Budget Committee has recommended, including a deficit of $115.4 billion for next year.

It called for deferral of the 1983 tax cut "until the current budget crisis has passed and interest rates have dropped to affordable levels" or replacement of the tax cut with "a fiscally prudent tax cut which distributes benefits fairly to all working and middle-class Americans"--all within the limits of a

07.2 billion tax increase over three years.

Hollings lost 17 Democrats and picked up five Republicans, including Sen. Charles McC. Mathias (R-Md.), who co-sponsored Hollings' proposal. Byrd got no Republicans and lost 10 Democrats, even though Senate Democrats as a group recently went on record as urging Reagan to reconsider his 1983 tax cut.

Among Washington-area senators, Mathias was joined by Sen. Paul S. Sarbanes (D-Md.) in support of Hollings' proposal. Only Sarbanes supported Byrd's amendment.

The assault on the tax cut came after Democrats failed to restore money that the committee had proposed to cut from education, health, environmental, cost-of-living increases for veterans benefits and other programs. Also defeated was a proposal to cut foreign aid.

The closest vote was on a proposal by Sen. Gary Hart (D-Colo.) to restore $931 billion over the next three years for programs for educationally disadvantaged children.

In the first vote on the issue, Hart lost, 51 to 48, with seven Republicans supporting his effort. He came closer on a reconsideration vote, losing, 51 to 49, only after Republican leaders succeeded in some arm-twisting on the floor.

Hart's proposal would have kept funding for the programs at their current levels. In the debate, he said only 45 percent of children eligible for the educational assistance were receiving it before last year's cuts of $400 million were implemented. The program, he said, "is fair . . . cost-effective and it works."

In the tax debate, Hollings said the deficit reductions that his tax increase would have produced were essential for lower interest rates, while Republicans argued that they were too much for an economy struggling out of a recession.

"I just don't believe the economy can stand that much . . . . I just don't believe the American people can stand that much," Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said, noting that the total amount of the three-year tax increase would be $183.5 billion, including the user fees, if Hollings' proposal were approved.

But Hollings contended that, if it were adopted, "the message would go out to the markets and everyone else, including Chairman Paul Volcker of the Federal Reserve, that the Congress has finally become serious about the problem" of reducing deficits, thereby easing pressure for high interest rates.

Hollings chided Republicans for picking up the old Democratic theme that deficits do not matter. "We got run out of office in 1980 with that kind of talk . . . " Hollings said. "These deficits do count."

Joining Hollings and giving the effort something of a bipartisan cast, Mathias argued that the tax cut amounted to "a sham transfer of money from the government to the consumers . . . just a transfer financed by budget deficits."

Added Mathias: "The whopping federal deficit just keeps staring Wall Street in the eye, so Wall Street has decided to watch and wait."

But Sen. William V. Roth (R-Del.), one of the principal architects of the tax cut, contended that any tampering with the cut would "only prolong the recession." The president, he added, "is keeping a steady course, and he is not going to permit his program to be gutted."

Meanwhile, the House braced for opening of debate today on several budget alternatives, with everyone hedging bets and Reagan taking a low-key, backstage role, at least for now.

Main alternatives include a Democratic-drafted plan recommended by the House Budget Committee, one prepared by House Minority Leader Robert H. Michel (R-Ill.) in consultation with some GOP moderates and Democratic conservatives and another bipartisan plan advanced by moderates of both parties.

Of the three plans, Michel's would cut most heavily into domestic spending and shave the least off Reagan's tax cuts and defense buildup. It is the closest of the three to the budget before the Senate and is closer to Reagan's original budget than any other House version.

As the House Rules Committee set ground rules for the debate, Michel said Reagan had made a few phone calls to Republican House members but has not yet been asked to do more.

"You don't use your ace in the hole until you really have to," Michel said, although he indicated that the president's card may have to be played eventually. "We're on the margin as far as votes are concerned . . . . It's very fragile out there," he said.

Michel acknowledged that support for Reagan's budget priorities is far less strong than last year when the president won dramatic budget and tax victories with unified Republican and conservative Democratic backing. "I wouldn't have gone through all this work if I didn't think we had a shot at it," Michel added.

Michel conceded that some "Gypsy Moth" Republicans from the Northeast and Midwest want to vote for the moderates' alternative but said he believes they will also support his plan. Under the Rules Committee's ground rules, they will be able to vote for both alternatives. The plan guarantees the Republicans, and just about everyone else, a vote on their own budget plans.

At the White House, deputy press secretary Larry Speakes acknowledged that Michel's proposal is "close to what we can support in most respects" but added, "We are not actively involved."