WASHINGTON (AP) _ The Democratic chairman and ranking Republican on the Senate Finance Committee today pledged swift action as the panel drafts tax increases to help achieve $76 billion in deficit cuts over two years.

The Reagan administration, meanwhile, is urging the committee to drop more than a third of the tax increases in its deficit-reduction package, including a boost in the payroll tax on 8 million workers.

But both Sen. Lloyd Bentsen, D-Texas, the chairman, and Sen. Bob Packwood, R-Ore., the ranking minority member, said they wished White House and congressional negotiators had requested bigger reductions in the federal budget's red ink.

''I think it's going to be easy for our part of the package,'' Packwood said of the committee's charge to find $23 billion in new tax revenues. ''My disapointment is that the whole package when it's all done is so much less than we should have done.''

Bentsen, interviewed along with Packwood on CBS-TV's ''This Morning'' program, expressed hope the committee would complete its work this week, but added, ''We should have gone for much more.''

If the administration successfully presses its request to substantially cut proposed tax increases, the committee might be forced to look at other taxes - including higher excise taxes on alcohol and tobaccco - to make up the difference. But there is no indication that will happen.

Treasury Secretary James A. Baker III arranged to meet with the committee today to spell out specific objections to the tax-increase bill that the panel approved in October. The deficit-reduction plan that the committee hopes to approve this week is likely to be built around the October bill.

That means it will not include any increase in income-tax rates.

President Reagan, meanwhile, said in a letter to House leaders Tuesday that he will have ''no hesitation'' in vetoing the huge spending bill expected to come to the floor for consideration Thursday, if the bill is not brought into line with the deficit-reduction pact.

In a letter to House Speaker Jim Wright, D-Texas, and House Minority Leader Robert Michel, R-Ill., Reagan said the current version of the bill ''clearly violates both the spirit and the terms'' of the deficit-reduction agreement.

House officials have said, however, that they intend to amend the bill to conform with the agreement.

The provision in the tax-increase bill affecting the greatest number of individuals would extend for three years the expiring 3 percent tax on telephone service. Most of the burden would fall on upper-income people and corporations.

The administration contends the limited increase in the payroll tax, which finances the Medicare program, could be especially harmful to small business. Half the tax increase would be paid by every employee earning over $45,000 a year and half by the employer.

Under present law, the Medicare tax of 1.45 percent applies only to the first $45,000 of wages that a worker earns in 1988. The provision in the Finance Comittee bill would eliminate that wage ceiling and apply the tax to all earnings. That would bring in $8.5 billion over two years.

The administration dislikes several other provisions, including one that would repeal the ''completed-contract'' accounting method, a special benefit for defense contractors. The Treasury Department also may oppose a section that would repeal tax benefits available to manufacturers, real estate dealers and others that sell on the installment plan.

Dropping provisions to which the administration has announced its opposition would knock $12.3 billion from the two-year, $30.8 billion tax increase the committee approved in October. Striking the installment-sales provision would cost another $4.6 billion.

A $76 billion, two-year deficit-cutting agreement reached last month by Reagan and congressional leaders requires a $23 billion tax increase. The committee's task is to decide which taxes to raise.

As part of their contribution to cutting the deficit, Finance Committee members are forgoing a jealously guarded perquisite: the right to add special tax-cut amendments to major tax bills. The panel is reluctantly agreeing to drop from the package any provision that would not cut the deficit.

''There was a lot of moaning - including on the part of the chairman,'' Bentsen told reporters after Tuesday's closed-door session. ''But that's part of the deal'' with Reagan.

The agreement would bar, for example, Bentsen's proposal to repeal the ''windfall-profits'' tax on the oil industry.

Also falling by the wayside would be dozens of such relatively narrow amendments as those granting a special depreciation tax benefit to citrus growers; allowing owners of Individual Retirement Accounts to invest in state- issued coins; and giving special dispensation to municipal bonds issued by various jurisdictions for a variety of projects.

The agreement also would wipe out passage this year of a 600-page measure correcting errors in the huge 1986 tax-overhaul law.

Despite the lack of appeal in raising taxes and cutting many government programs, several congressional leaders predicted that lawmakers will approve a package this year.

Reagan's anti-deficit team - Treasury Secretary Baker, White House staff chief Howard H. Baker Jr. and James C. Miller III, director of the Office of Management and Budget - tried to sell the agreement to Senate Republicans over lunch Tuesday.

''I think there'd be a majority of (the) 46 Republicans who'd rally around this,'' said Sen. Alan K. Simpson of Wyoming, the assistant GOP leader.

''We didn't ask for any show of hands, but I'm of the opinion ... that this is the only package that has a real chance for passing the U.S. Senate,'' added Sen. Pete V. Domenici of New Mexico, senior Republican on the Senate Budget Committee.