Senate Finance Committee Chairman Bob Packwood (R-Ore.) said yesterday his committee will begin work on a tax-simplification plan as soon as one passes the House and that he expects to have a bill on President Reagan's desk by Christmas.

Packwood, House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) and other tax specialists appeared on a round of weekend television interviews two days before Reagan has scheduled a nationally televised address to outline his plan to lower tax rates while eliminating many special tax advantages.

Rostenkowski said yesterday that despite the long and complex process of rewriting the tax code, he hopes to bring a bill to the House floor by mid-October.

And although he said he is concerned that the president's proposal could fall short on "an ingredient of fairness," Rostenkowski said on NBC's "Meet the Press": "I'm not going to drag my feet."

Packwood, appearing on ABC's "This Week With David Brinkley," said, "We will be ready to move on this bill as soon as the House finishes."

Packwood said he expects the House and Senate to reconcile their differences by the end of November, and "We will have a bill to the president by Christmas."

The politically nettlesome process of overhauling the Internal Revenue Code began in November when the Treasury Department released a plan to lower rates and do away with many popular deductions. Over the last few months, the original plan -- now called "Treasury One" -- was revised partly in response to political pressures from groups as varied as oil interests and private charities.

As the president's plan moves to Congress, it will encounter what Rostenkowski yesterday called "535 independent contractors that all have an agenda of their own."

The White House has promised that Reagan will launch a nationwide sales campaign that officials say they hope will whip up public sentiment in favor of a sweeping tax revision and overwhelm interest groups trying to protect their breaks.

Despite the optimistic statements by Packwood and Rostenkowski, the outlook for tax revision is cloudy. Advocates have expressed disillusionment because of the delay in announcing the plan. And they say they are upset with some of the administration's compromises.

Some lawmakers are reluctant to take up "revenue-neutral" tax legislation because, by definition, it would not help reduce the federal deficit. And every endangered tax preference has at least one friend in the House and Senate pleading for a reprieve.

"The politics of tax reform is beginning to fade around here," said Rep. Leon E. Panetta (D-Calif.). "Everybody talks about tax reform, but nobody feels much is going to happen. The mood has soured somewhat."

The congressional tax-writing process will begin shortly after Reagan lays out his plan Tuesday night. Treasury Secretary James A. Baker III will testify before the Ways and Means panel on Thursday, and the hearings are to continue with corporate executives June 4. Rostenkowski said he plans to hold hearings through the summer and wants to begin drafting a plan soon after Labor Day.

Aides say Rostenkowski is determined to require that any amendment that loses revenue be accompanied by one that raises the same amount. And most of the hearings will be designed so that witnesses favoring the elimination of a tax break will testify on the same days as those opposed.

Packwood has said his hearings will run about two weeks behind Ways and Means. But he says it will be up to the House to pass a bill before the Senate -- generally considered more reluctant -- wades in. Also, under the Constitution, the House is supposed to originate revenue bills.

Members of both houses will be hard-pressed, however, to resist pleas from the many lobbies now preparing for the next phase of tax revision. The most powerful push is expected to come from state and local governments, whose representatives feel that the administration's rewrite of its tax plan appeased the private sector but turned a deaf ear to them.

The end of the deduction for state and local income, sales and real-property taxes is one of the big money items in the package. Ending the deduction would raise $34 billion by 1988 to help pay for tax-rate cuts.

So far, the outcry against the provision has been limited to officials from a few states where taxes are higher, principally New York. But that is expected to change as governors, mayors, city and state budget officers, school-board officials, public-employe unions, teachers' unions and state legislators begin to focus on the issue. Most have been busy until now fighting cuts in the budget.

Asked yesterday about the end to the write-off for state and local taxes, Packwood said, " . . . Every group, whether it's the city of New York or the steel industry or somebody else, has a particular concern with some portion of the bill. They've simply got to wait until it's over and look at the whole bill and say, 'Are you better off?' "

But already the deduction is the subject of three sets of hearings, and it is an example of how tax revision not only divides individuals according to their financial interests but also pits one section of the country against another.

"This bill is going to polarize the country along regional and economic lines on that issue alone," said former Republican congressman Barber B. Conable Jr. of New York, now with the American Enterprise Institute.

Numerous non-governmental lobbies, including insurance, real estate, oil and gas, investment firms, educational institutions, charitable organizations, benefits providers and capital-intensive industries, will also look for relief from Ways and Means and Finance.

Many have learned from the success of financial institutions in repealing tax withholding on interest and dividends in 1983 and will use broad-based mass-mail campaigns. The idea is to whip up public sentiment against removal of tax breaks that otherwise would not raise anyone's ire, such as taxation of the increase in value of life-insurance policies. Already, those efforts appear to be producing results.

"Our mailroom is working overtime trying to keep up with the mail opposed to provisions of Treasury One," said Ways and Means member Willis D. Gradison Jr. (R-Ohio), who said he supports some form of tax revision. "I'll bet I haven't received half a dozen letters in support of it."

Sen. Lloyd Bentsen (D-Tex.) said his office has received more than 6,000 letters against portions of the first plan and fewer than 100 in favor of it.

Reagan's sales campaign is designed to change that, telling Americans that they will benefit overall from lower rates even if they lose some deductions. But during the months of delay, the chief backers of tax overhaul in Congress have lost some heart.

Rostenkowski, for instance, has openly criticized the administration for taking away his bargaining chips by restoring a number of controversial changes in Treasury One.

Sen. Bill Bradley (D-N.J.), among others, has said he worries that Republicans in the Senate will stall the effort. Rep. Jack Kemp (R-N.Y.) and Sen. Robert W. Kasten Jr. (R-Wis.), both from high-tax states, say they cannot accept the plan's top rate of 35 percent, combined with the loss of deductions for state and local taxes.

All of those legislators say they remain committed to reworking the tax code and that the time has never been better or presidential commitment greater to a tax overhaul.

And administration officials say another factor will push Congress into a tax bill: The final package has to bring in the same amount of revenue as the current code. High deficits would make revenue-losing tax cuts difficult, and Reagan has said he is adamantly opposed to any tax increase. That combination will make it hard for legislators to tamper much with the administration package, officials said.

"If you take anything out, you've got to put something back in, or raise the rates or lower the personal exemption," said a Treasury official. "I think they will find they will have a hard time doing those types of things. I think they will find themselves under the same pressures we were under."