President Reagan tried again today to revive lagging public interest in his tax overhaul proposal, but a new Washington Post-ABC News poll indicates that the president's efforts so far have not been successful.

And in part reflecting the lack of public pressure for overhaul of the tax code, Senate Republicans, meeting in a closed caucus, voted overwhelmingly against attempting to pass tax revision this year if it means remaining in session through December to do so.

But the Democratic House is continuing its efforts on the package, where passage this year is still predicted. The Ways and Means Committee is scheduled to begin substantive work on the plan Thursday although the committee staff is having difficulty producing promised alternatives to Reagan's proposal.

In Tennessee, on one of a series of tax-revision promotion trips Reagan has given since Labor Day, the president warned that the economy is likely to turn sour unless the tax proposal is approved.

" . . . Tax reform is a drama with heroes and villains and a damsel in distress," Reagan said to a flag-waving crowd of several thousand in the county courthouse square here. "The heroes are the citizens across this country who are asking for tax justice. The villains are the special interests -- the 'I got mine' gang. And the damsel in distress? A lass named Endless Economic Growth, who's tied to the tracks and struggling to break free."

The presidential rhetoric, however, does not seem to have dented public attitude on tax overhaul. The Washington Post-ABC News poll showed an even split among those who favor and those who oppose Reagan's proposal, 22 percent on each side.

A majority of those polled, 56 percent, didn't know enough about the plan to have an opinion or were undecided. The poll also found that, for the first time since January 1983, more people expect the economy to worsen rather than improve.

That compares with a June poll in which more of those questioned, 26 percent, favored the Reagan proposal, and fewer, 14 percent, opposed the plan. About 60 percent had no opinion. That poll was taken shorly after the president launched his tax-overhaul campaign in a nationally televised speech on May 28 in which he called the plan the "second American revolution." The new poll was taken Sept. 19-23.

The issue virtually disappeared from public view in the summer during the TWA hijacking crisis in Beirut last June and Reagan's cancer operation in July. Then, in August, the president took three weeks' vacation in California, and his advisers announced that he would try to build support for the tax overhaul in a "fall offensive" beginning Labor Day.

Since then, Reagan has spoken in Missouri, North Carolina, Florida and New Hampshire on behalf of the tax overhaul, the major domestic initiative of his second term. He has been greeted with friendly crowds, as he was today, but even some of his aides say that his largely repetitive speeches have failed to build a groundswell of popular support.

Reagan insisted today, however, that his proposal has strong public backing.

"I've been going all over the country talking about tax reform -- and wherever I go the people tell me they are frustrated by the current system and they back our plan . . . , " Reagan said.

Reagan called for passage of the tax plan by the end of the year but avoided partisan or anticongressional rhetoric, part of a White House strategy to take a conciliatory approach.

"It's a deliberate softening of the rhetoric," a senior official said. "We're trying to work with the Congress rather than bludgeon anyone."

The official said the administration hopes that the Democratic-controlled House can be nudged to speed up action on the tax bill and that Senate Majority Leader Robert J. Dole (R-Kan.) then will persuade senators to stay in session some extra days to complete action on the measure.

But that prospect dimmed today in the Senate Republican caucus when Sen. Dan Quayle (R-Ind.) asked for a show of hands on the issue of extending the work session beyond the tentative Thanksgiving adjournment.

Quayle said afterward that only seven or eight senators of about 40 present voted to stay in session through December. "The rest said no. Some said, 'Hell, no,' " he said.

He said senators were responding to lack of pressure from constituents for tax revision and to a belief that there is not sufficient time left in the session to complete the work.

After the caucus, several senators said deficit reduction was of far more concern than any other issue, including tax overhaul and trade. "Tax reform or trade are way down on the Richter scale," Republican Conference Chairman John H. Chafee (R.I.) said.

If anything, he said, interest in tax reform has waned. "It's not catching on. If it did excite the American people, it isn't exciting them anymore," Sen. Thad Cochran (R-Miss.) said.

The informal vote underscored support among Republicans for the position taken by Dole, who declined to comment on the actual vote, except to say it confirmed what he had been hearing from his colleagues. "I want the White House to know I just don't dream up this stuff. My ears are pretty good. I hear," he said.

Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) plans to offer alternatives to key elements of the Reagan tax proposal at the panel's meeting Thursday, but committee aides are struggling to produce alternatives that would not increase the deficit.

One of the sticking points is the deduction for state and local taxes, which the Reagan proposal would terminate. Rostenkowski is considering a compromise that would let taxpayers either deduct those taxes up to a flat-dollar amount, such as $750, or deduct only those taxes that exceed a set percentage of income.

Such a compromise would ease loss of the deduction for residents in the lowest- and highest-tax states.

Other possibilities include scaling back business writeoffs for new plants and equipment while abandoning Reagan's controversial proposed tax on companies that have made heavy use of such deductions and eliminating Reagan's proposal to tax the first few dollars each month of health insurance premiums paid by employers.

The Rostenkowski proposals, intended to be a starting point, would cover about 30 percent of the elements in the Reagan plan, sources said.