Congressional leaders yesterday promised swift Senate action on the giant tax-overhaul legislation approved unanimously by the Senate Finance Committee, as the measure drew support from legislators across the political spectrum.

Politicians as different as liberal Sen. Edward M. Kennedy (D-Mass.) and conservative Rep. Jack Kemp (R-N.Y.) praised at least the general outline of the committee bill, which would reduce rates in exchange for eliminating many popular tax breaks -- a sign of the measure's early political acceptability.

The bill would cut the top personal tax rate nearly in half, to 27 percent, and reduce the corporate rate by a third, to 33 percent. The measure's principal author, Finance Committee Chairman Bob Packwood (R-Ore.), said yesterday that he expects "a broad coalition" of consumer, labor and business groups to lobby for the measure.

Senate Majority Leader Robert J. Dole (R-Kan.) said, "We're going to bring it up as quickly as we can," and he predicted that there would be few major changes in the bill approved by the committee in the early morning hours yesterday.

One factor that may prove him right, congressional sources said, is procedural restrictions imposed by the Gramm-Rudman-Hollings balanced-budget law. Because amendments to restore tax deductions would cost federal revenue, increasing the deficit, they could be barred unless they are coupled with offsetting tax increases elsewhere.

Packwood said this constraint could be "tremendously helpful" in disciplining senators who want to restore deductions but do not want to raise tax rates above the levels in the bill. But he faces one difficulty: The amendments technically would not be out of order until Congress agrees on a budget resolution for fiscal 1987, and the House is only now beginning its budget process.

One unknown ingredient, senators said, will be the effect of television on Senate consideration of the tax bill. Senate proceedings on C-Span begin June 1, about the time Senate leaders hope to bring up the measure.

"It's going to be difficult to see someone up there arguing on TV before millions of people that we ought to curtail IRAs Individual Retirement Accounts or the deductibility of interest on consumer loans," said Sen. Lloyd Bentsen (D-Tex.).

Powerful interests are preparing to fight portions of the committee bill. Bentsen said his office is beginning to receive many telephone calls from constituents who have been notified by large banking and investment firms that their IRAs would be curtailed. (The bill would end IRA deductions for taxpayers covered by other pension plans, although interest on these deposits would remain tax-deferred. For those without other pension plans, IRA provisions would not change.)

Amendments are expected to be offered to retain the full deduction for IRAs, to restore the deduction for state and local sales taxes and to raise the top rate in the plan to 35 percent, among others.

The real estate industry will also mount a formidable lobbying effort to alter the committee bill to restore numerous tax breaks for investors in commercial and residential property.

As adopted by the Finance Committee, the tax measure would virturally wipe out the real estate partnership business that has created a commercial building boom in Washington and many other cities.

Industry spokesmen claimed yesterday that the committee bill would cause widespread bankruptcies and a halt of all new construction. Related story, Page E1.

However, despite the bill's more controversial provisions, the blanket opposition to tax overhaul that was apparent among some senators when it was languishing in the Finance Committee a few weeks ago seems to have evolved into more specific objections. Sen. Alfonse M. D'Amato (R-N.Y.), for example, was once so opposed to the measure that he raised an official objection to a request to have the Finance panel take votes.

Now, a spokesman said, D'Amato "thinks they're doing a pretty good job. This bill has changed dramatically from what they were talking about doing before."

Besides reducing rates and limiting IRAs, the bill would eliminate the deduction for interest on consumer loans, such as those for autos and credit-card purchases. Interest on mortgages for up to two homes would remain deductible, as would charitable contributions for those who itemize their deductions and non-sales state and local taxes.

It would increase the personal exemption for taxpayers and dependents to $2,000 by 1988 for all but the highest-income taxpayers and would raise the standard deduction for those who do not itemize.

A controversial change, expected to be the subject of heavy lobbying, would end low effective tax rates on capital gains.

The measure would raise corporate taxes by more than $100 billion over five years and cut individual taxes by the same amount. The average tax reduction for individuals would be 6.2 percent, with the biggest proportional tax cuts going to low-income taxpayers.

Those broad outlines are similar to the tax-revision bill the House passed last December, but the House measure would transfer about $140 billion in taxes to businesses and give individuals a larger tax cut. The House plan retains more individual deductions, but has four brackets and a top rate of 38 percent for people and 36 percent for companies.

House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.), in his first statement on the Senate's tax-revision efforts, said the Finance Committee bill "has suddenly given tax reform enormous drive. The spirit and thrust very nearly parallel the House-passed bill."

House Minority Leader Robert H. Michel (R-Ill.), who had problems with the House tax measure, said the chances of Congress passing a tax bill "have been significantly improved."

Sen. Daniel Patrick Moynihan (D-N.Y.) and others pointed out that the 20-to-0 roll call vote in committee after midnight yesterday will give the legislation strength.

Looking past Senate passage, Packwood predicted that a House-Senate conference will "marry the best of both bills." Sen. Russell B. Long (D-La.), who was chairman of the Finance Committee for 14 years and is the panel's ranking Democrat, was a little more pragmatic about the amendments, or riders, expected on the Senate floor.

"A strong horse can carry a lot of riders, but usually the riders drop off in conference," Long said.