President Reagan and the Republicans have fumbled away the tax-reform issue, political strategists of both parties said yesterday, but it's not clear whether the Democrats can score points on the break.

While some strategists in both parties expressed skepticism that many voters will know or care who blocked the tax initiative Reagan put at the top of his domestic agenda, White House and Republican campaign officials said they thought it essential to rewrite the record of near-solid GOP opposition in the House last Wednesday.

Rep. Guy Vander Jagt (R-Mich.), chairman of the Republican Congressional Campaign Committee, said Thursday it "is very, very important" to Republicans that they find a way to bring the year-long Reagan effort -- left in a state of suspended animation over the weekend -- back to life in the House next week.

Vander Jagt, who joined with 163 of the 182 House Republicans in voting down the procedural motion for considering the Democratic tax-overhaul bill and the GOP alternative three days ago, was having second thoughts yesterday. "It appears today that it's the Democrats who support tax reform and the president," he said. "That's not the fact, but only by getting the issue up again and having a big vote for the Republican alternative can we make it clear we're for tax reform and have a better way of getting it accomplished."

As negotiations continued yesterday, it was not clear whether Republicans would get that second chance. But White House strategists said a compromise was essential, not just to save the president's pet program but to preserve GOP seats in the 1986 election and long-term hopes for party realignment.

Mitchell E. Daniels Jr., the president's assistant for political affairs, said that "if it's left where it is, there will be an interpretation, fair or unfair . . . that the Republican Party is more concerned about abstractions like capital formation than realities like taxes on working people, more concerned about corporate balance sheets than getting poor people off the tax rolls.

"Under the president's leadership," Daniels said, "we've been successfully moving away from that myth, but this may bring it back."

Democrats were doing their best to make that fear a reality. Paul G. Kirk Jr., chairman of the Democratic National Committee, spoke scornfully to reporters at breakfast about earlier White House talk of "a fall offensive on the great realigning issue of tax reform." When it came to a vote, he said, "the Republicans wouldn't go along" because tax overhaul "struck at the heart of their base in the giant corporations."

Kirk and Martin D. Franks, executive director of the Democratic Congressional Campaign Committee, said that the failure on the tax bill, which raised doubts about Reagan's mastery of Congress and damaged his relations with his party's leaders on Capitol Hill, was the symptom of a squandered reelection landslide and a portent of a Democratic comeback in 1986.

"Now," said Franks, "we've got the better end of the tax-reform argument, we still have Social Security, they've done very little to take away the trade issue. We've got a powerful issue in their fiddling around with the farm problem, and they still haven't begun to solve the deficits. We come out of 1985 not half bad, considering where we started."

Kirk pushed the argument further, embellishing the claim of House Speaker Thomas P. (Tip.) O'Neill Jr. (D-Mass.) that the Republican rebellion against the tax bill marked the onset of "lame duck" status for Reagan.

"His No. 1 legislative priority lies in rubble," Kirk said, adding that Reagan now has "very little relevance" on domestic issues.

That judgment was strongly rejected by Republican strategists, but some of them said they worried about the growing distance between Reagan and his party leaders in Congress. One longtime political adviser, now outside the government, said there was no sign in the handling of the tax issue of the coordinated legislative-political strategy Republicans will need in 1986 to break the historical pattern of mid-term election losses by the president's party. Another, who said the revolt would hurt the perception of Reagan's power among Washington insiders, said Republicans appeared to be suffering as much "dealignment of solidarity" with their leaders as Democrats.

But others said that any "lame duck" judgment on Reagan was premature. Robert Teeter and Richard Wirthlin, leading GOP pollsters, and Greg Schneiders, a Democratic campaign consultant, said Reagan's apparent failure on the tax issue reflected more the public skepticism and indifference toward that issue than any loss of his power.

"He took on a very tough issue, and he lost on it," Teeter said, "but I don't think he will ever be a lame duck, if that implies that he's lost his grip on the country."

Schneiders, who was a White House official when President Jimmy Carter tried unsuccessfully for a major overhaul of the tax code, agreed that when tax reform is separated from tax reduction, "it's a loser of an issue." But turn Reagan loose on "foreign policy or a more popular kind of domestic issue," he said, "and he has just as much power to move public opinion as he ever did."

Because of the low levels of support and interest most polls have shown on tax reform, many of the Republicans who voted against the president on Wednesday's procedural test said they felt little risk of political backlash.

But Democratic consultants Robert Beckel and Peter D. Hart said they could envision Democratic challengers to Republican incumbents running ads saying, "When he had to choose between the president and the special interests on tax reform for middle-income people, my opponent voted with the special interests."