The White House yesterday expressed "serious reservations" about the fiscal 1987 budget adopted by the Republican-controlled Senate, but House Democrats cautiously praised the spending plan and suggested that it is close to what Congress will adopt.

House Budget Committee Chairman William H. Gray III (D-Pa.) called the Senate plan "more realistic and fair than the president's original request." He and other House Democratic leaders, who were waiting for the Senate to move first on the budget, are expected to wrap up their version quickly. Gray said he intends to call a committee drafting session next week.

The $1 trillion budget approved early yesterday by a big bipartisan majority in the Senate calls for twice the tax increase that President Reagan seeks and about half the domestic spending cuts and defense spending increases that he seeks.

The measure, which cleared its crucial first vote 38 to 13 among Republicans and 28 to 16 among Democrats, meets the $144 billion deficit target of the Gramm-Rudman-Hollings budget-control law. Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) said its implementation by Congress and the White House would make unnecessary any automatic spending cutbacks next fall.

But he and Sen. Lawton Chiles (D-Fla.), who together sponsored the compromise, emphasized that Reagan's support will be needed for the tax and spending measures necessary to meet the budget targets.

After extensive maneuvering and negotiations spearheaded by Senate Majority Leader Robert J. Dole (R-Kan.), the budget came closer to Reagan's goals than an earlier plan from the Senate Budget Committee -- but not close enough to draw an embrace from the White House.

"While the president has serious reservations about individual aspects of the Senate budget resolution, he believes it is important that the Senate pass a budget for 1987 and recognizes their effort," said presidential spokesman Larry Speakes, en route with Reagan yesterday from Indonesia to Tokyo.

"It's not exactly what we wanted, but it's part of the process," Speakes added.

He said the administration will "work through the authorization process and in the House to shape the budget more to our liking" and will consider vetoing spending bills that exceed administration targets.

Speakes indicated that the president is particularly distressed at the tax provisions. The plan calls for tax increases of $13.1 billion next year -- including cigarette and other smaller levies already approved -- and totaling roughly $50 billion over three years. The Budget Committee had recommended fiscal 1987 tax increases of $18.7 billion, including about $6 billion in miscellaneous revenue increases proposed by Reagan.

Speakes said the budget also "falls short of the president's requested levels for providing a strong defense" and calls for domestic spending reductions that are "more modest than what the president feels are appropriate."

The Senate budget would raise defense spending authority from $287 billion to $301 billion, or $19 billion less than Reagan said is needed. He seeks to increase the military budget by about 8 percent after inflation. The Senate figure is expected to allow modest growth beyond inflation.

On the domestic side, about $8 billion in savings was added to the committee plan, more than half of it from re-estimating costs because of lower-than-expected inflation. Federal pay and pension cost-of-living increases were adjusted downward, for example, from 3.4 percent to 2 percent to reflect the lower inflation estimates.

But some domestic spending was added, and termination orders for eight or nine minor programs were withdrawn at the last minute. Instead, a lump sum of $41 million was designated for program cutbacks or "possible terminations," with no specific programs targeted for extinction. Reagan had wanted to kill 44 programs. The Budget Committee had proposed killing three, but the Senate resurrected one, the Work Incentive Program for welfare recipients.

A critical question facing the House Budget Committee next week will be whether to include a tax increase in its plan. Democratic leaders once said they would consider a tax increase only if Reagan proposed it, then indicated they might consider it in league with both House and Senate Republicans.

"I think we have given to the House Democrats what they needed, and that's a budget that has a majority of Republicans supporting new taxes," said Chiles. "I don't think they have to wait for the president to say he'll take new taxes."

House Minority Leader Robert H. Michel (R-Ill.), described by some House Democrats as a crucial figure in achieving a bipartisan agreement on taxes in the House, issued a statement congratulating the Senate but avoiding comment on specifics of its budget plan.

Senate passage of the budget was a triumph for Domenici and Chiles, who had gone out on separate political limbs to draft a bipartisan budget in the committee and then stayed together as they negotiated modifications to win more votes, especially from Republicans.

It also may have given Dole, pulled in different directions by the White House and assorted factions within the Senate GOP, what he needed to get out of a tight spot -- both as leader of the Senate and as a possible candidate for the Republican presidential nomination in 1988. He had held out for more than a month to win concessions for the White House and Senate conservatives and achieved his goal of heavy Republican support for the compromise. He avoided both a public break with the White House and a personal rift with his friend and ally Domenici.

Both Reagan and the Democrats also came out with more than budgetary crumbs. Reagan picked up $6 billion for defense, a few more domestic spending cuts and less in the way of tax increases. And an obstacle to consideration of his tax-overhaul plan was removed for Republicans who were refusing to consider it before a budget agreement was reached.

Largely because their votes were necessary for passage in light of GOP divisions, Senate Democrats had more of an impact on this budget than any other in the six years of Reagan's presidency. Sen. William L. Armstrong (R-Colo.) even went so far as to say that Walter F. Mondale, who proposed tax increases during his unsuccessful challenge of Reagan in 1984, may have won the tax fight after all. "Mondale won, it's as simple as that," groused Armstrong. "Our team blinked."