Little more than a week after Congress passed deficit-reduction legislation designed to compel the Reagan administration to compromise on spending and taxes, there are signs that the strategies of Democratic lawmakers may backfire on them.

Not only has President Reagan intensified his already strong rhetoric in opposing higher taxes and lower defense spending, but Democratic tax-writers have run into early and stubborn resistance from Republican lawmakers whose help is needed to pass legislation raising new revenues.

"To those who say we must weaken America's defense, they're nuts," Reagan said on Wednesday as he signed legislation that bolsters the Gramm-Rudman-Hollings balanced-budget law by requiring automatic budget cuts if new deficit targets cannot be reached through separate legislation. "To those who say we must raise the tax burden on the American people, they, too, are nuts."

The following day, in a show of solidarity with their president, House Republicans on the Ways and Means Committee essentially refused to take part in the first mark-up session devoted to crafting a $12 billion tax increase Democrats want as part of a $23 billion deficit-reduction package.

Although Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) predicted that Democrats could, with difficulty, write a tax bill on their own, others were less sure about the outcome in the full House.

"The question is whether we can fashion one that will pass the House floor," said Rep. Ed Jenkins (D-Ga.). "There are a lot of members saying let's just take" the automatic spending cuts.

Those developments may signal an eventual defeat for the Democratic strategy of forcing the president to cooperate in raising revenue by threatening a continued slowdown in his defense buildup. To some on Capitol Hill, it seems increasingly likely that Reagan will accept the $23 billion across-the-board cut threatened by the new budget law -- half of it from defense -- rather than give in to higher taxes.

The net effect, given the spending patterns of the last six years, could be that the Democratic strategy boomerangs and ends up hurting domestic spending programs important to the party's constituencies more than it harms the Pentagon.

Some lawmakers are genuinely concerned about the prospect of across-the-board cuts. Sen. Sam Nunn (D-Ga.), the chairman of the Senate Armed Services Committee, said Friday that the projected automatic reductions would cause "all-out chaos" for the defense budget.

But other legislators say that because of the Reagan defense buildup and the resulting steep reductions in discretionary domestic spending during the first six years of the president's tenure, the impact would fall most heavily on programs that benefit the middle class and poor.

"The whole thesis was that the president would accept a tax increase rather than take the cut in defense, but I'm not sure the thesis holds," said Rep. Charles E. Schumer (D-N.Y.), a liberal who opposed the Gramm-Rudman-Hollings repair.

"I think {the Pentagon} is awash in extra money," Schumer said. "The Pentagon is like a squirrel's lair -- there's lots of little acorns hidden away. The programs that will be hurt the most are the programs Reagan has already slashed: housing, social programs, urban programs."

An analysis of the impact of the $23 billion automatic cut released Friday by the Senate Budget Committee, based on Congressional Budget Office figures, bolsters that argument.

The effect on defense varies depending on whether Reagan accepts the option offered under the law of protecting military personnel from the reductions. If he does, and many believe he would, the cuts would fall more heavily on weapons procurement, research and development, which are areas of Pentagon spending that have risen most dramatically in recent years.

If Reagan shielded personnel, defense spending authority would be set at around $280 billion, or $9 billion less than last year's level, well short of what is needed to keep pace with inflation. If personnel absorb their share of the cuts, the spending authority is reduced to $285 billion, or $4 billion less than last year. In his budget, Reagan requested $312 billion.

Gordon Adams, director of the Defense Budget Project of the Center on Budget and Policy Priorities, said that cuts of that magnitude would be significant but hardly disastrous for a Pentagon whose budget has almost doubled, without adjusting for inflation, since Reagan took office.

"There would be a little blood on the floor, but it would force them into some choice-taking which they've been able to avoid until now," Adams said.

To some degree, White House officials agree that they can live with the impact. "The president just isn't going to sign a tax hike, and it's clear now that he isn't going to have to," said one official in assessing the threat of Gramm-Rudman-Hollings.

There is also a widespread expectation, both in the administration and Congress, that the president could further mitigate the hit on defense with a supplemental spending bill early next year.

On the domestic side, where discretionary spending fell by 21 percent between 1981 and 1987 on an inflation-adjusted basis (compared to a 40 percent increase in defense, also adjusted), the impact may be more severe.

Because many entitlement programs such as Social Security are exempted or partially shielded from the automatic cuts, the brunt falls on discretionary spending in such areas as housing and education.

According to the analysis prepared by the Senate Budget Committee, the automatic reductions would cut in fiscal 1988:$900 million from education, training and employment programs; $1.1 billion from agricultural assistance programs; $800 million from transportation, including mass transit and highway aid; $600 million from health programs, including basic research, AIDS and drug abuse; $300 million from various veterans' programs; $700 million from income security programs including housing subsidies; $200 million from community development.

Surveying that fiscal landscape on Friday, Senate Budget Committee Chairman Lawton Chiles (D-Fla.) and the panel's ranking Republican, Pete V. Domenici (N.M.), almost begged for a high-level meeting involving the House, Senate and White House to find a compromise.

"If we can negotiate with the Soviet Union. . . to reduce nuclear weapons, we ought to be able to negotiate among ourselves to reduce the deficit," said Chiles.

"Somebody, someplace has to offer a solution to this," Domenici added.

Although one administration official said the White House has not totally given up hope of such a compromise, it is viewed as "a long shot" that depends on Congress showing a willingness to cut domestic spending.

House Republicans agree. "Most of us aren't objecting to a revenue component," said Rep. Willis D. Gradison Jr. (R-Ohio), "but we want some meaningful spending cuts."Staff writers Lou Cannon and Anne Swardson contributed to this report.