President Trump, Vice President Mike Pence, the House speaker Paul Ryan and the Senate majority leader Mitch McConnell at the White House yesterday. CreditAl Drago for The New York Times

WASHINGTON — The sweeping tax overhaul approved by Congress this week hands Republicans a long-sought achievement they believe will bolster their defenses in next year’s midterm campaign, but party officials concede the measure may only mitigate their losses in what is shaping up to be a punishing election year.

While the tax legislation is broadly unpopular as it reaches President Trump’s desk, the bill offers Republicans the sort of signature accomplishment they have been lacking to galvanize their demoralized donors and many of their voters.

Republican lawmakers, who spent much of this year forced to explain or defend Mr. Trump’s erratic behavior, now have an opportunity to go on the offensive with an issue that unites their increasingly fractious party. And they hope that up-for-grabs voters will reward them should the economy keep growing while their tax bills are falling.

“Once the withholding tables change in January, voters will realize their paychecks are bigger as a result of tax reform,” said Representative Steve Stivers of Ohio, who runs the House Republican campaign arm. But, alluding to past midterm defeats for the party in power at the White House, he acknowledged that “history is against us.”

To reinforce the party’s message, the primary House Republican “super PAC,” the Congressional Leadership Fund, is planning a $10 million advertising and grass-roots campaign beginning next month in some of their most competitive districts to highlight the rate reductions, higher standard deduction and child tax credits in the bill. Corporations such as AT&T and Wells Fargo delivered Republicans an immediate gift by announcing they would reward employees financially because of the tax cut.

Senator Mitch McConnell of Kentucky, the majority leader, said in an interview that Senate Republicans next year would batter the many Democrats who are on the ballot in states won by Mr. Trump, such places as North Dakota, West Virginia and Indiana, for opposing the bill.

Yet with voters indicating by wide margins they prefer Democrats to control Congress and bestowing Mr. Trump with historically low approval ratings, the tax plan is hardly a panacea for Republican lawmakers on the ballot in 2018. At best, it is the political equivalent of tacking up plywood against exterior windows to lessen the inevitable damage of an impending storm.

Officials in both parties believe Democratic gains in the House, where Republicans enjoy a 24-seat majority, could reach as high as 40 seats if the political environment does not improve for the Republicans.

And, as of now, it only appears to be worsening.

A CNN poll released on Wednesday found that 56 percent of registered voters said they would vote Democratic next November, compared to 38 percent who favored the Republicans, a yawning 18-percentage-point gap that was only slightly bigger than other recent polls. Through that lens, impressions of the new tax law could be warped by partisan feelings.

This advantage is showing up in fund-raising, where Democrats are harvesting small-dollar contributions. The Democratic Congressional Campaign Committee announced on Wednesday that it raised $6.9 million in November, outraising its Republican counterpart for the seventh month in a row. In November, the National Republican Congressional Committee raised only $3.8 million.

House Republicans, however, still have more money on hand and the Republican National Committee has far more cash than the Democratic National Committee. In the Senate, the Democratic campaign arm has slightly more money in the bank than the Republicans.

Beyond the raw numbers, Democratic enthusiasm is soaring. And the sort of centrist voters that both parties covet are contemptuous of Mr. Trump because of his behavior and character, elements that are highly unlikely to change by next fall no matter what policies emerge from Washington.

“The downside of doing nothing was much higher,” former Representative Thomas M. Davis III, a Virginia Republican who previously led the party’s House campaign efforts, said of the tax bill. “But the major problem for Republicans is not that they haven’t delivered — it’s the way he conducts himself.”

“Republicans have a big storm coming at them,” he added. “We just don’t know if it’s a bad wind storm or a Category Five hurricane.”

Mr. Trump has the lowest approval rating of any modern president this soon into his tenure, and midterm elections are inevitably referendums on the party that controls the White House. He is especially unpopular among women, who in this year’s statewide and special elections have overwhelmingly supported Democrats. According to a new NBC News-Wall Street Journal poll, 62 percent of female voters disapproved of Mr. Trump.

Kevin McCarthy, the House majority leader, before a vote on the tax bill yesterday. House Republicans still have more money on hand and the Republican National Committee has far more cash than the Democratic National Committee. CreditAl Drago for The New York Times

So Democrats, some of them still bearing wounds from President Barack Obama’s midterm losses, believe the tax measure will ultimately be of little consequence compared to the man who occupies the Oval Office.

“You can’t run from the top of your ticket,” said Representative Rick Larsen of Washington, who got a scare in the Affordable Care Act-fueled backlash of 2010. “That’s been proven to me over and over again. And the driver won’t be the tax cut vote. It’ll be the unpopularity of the president.”

There is also scant evidence large-scale tax bills offer much in the way of a political lift. Republicans suffered losses in 1982, a year after President Reagan’s first tax bill, and in 1986, just a few months after Congress passed the last tax overhaul. The 2002 gains by Republicans were more the result of a rallying around the commander-in-chief in the months after the attacks of Sept 11, 2001, than the tax cuts that the party passed a year earlier.

Mr. Obama’s economic stimulus plan of 2009 included tax cuts that went straight into paychecks — and were hardly noticed ahead of the Republican Tea Party tidal wave in 2010.

Complicating matters for Republicans, some of their House seats that are most in jeopardy are in high-income and high-tax states where many voters will feel little benefit from a bill that limits mortgage interest deductions and state and local tax write-offs. Eleven of the 12 House Republicans who opposed the bill hail from California, New York and New Jersey, most of them from affluent districts that are already uneasy with Mr. Trump.

“I think each individual congressman will be judged on how they voted,” said Representative Dan Donovan, the only Republican who represents New York City, who opposed the measure because of the limitations on local tax deductions. “The voters will know how hard we fought.”

Yet as the fallout from the Affordable Care Act demonstrated in 2010, when half of the 34 House Democrats who opposed the measure still lost their re-election, opposing a controversial bill is not enough to inoculate lawmakers in wave election years.

“The wave starts in those districts whether they voted for or against the tax bill,” said former Democratic Representative Steve Israel of New York, calling this moment “political déjà vu.”

Notably, the House Republicans who opposed the bill also will not be the beneficiaries of the Super PAC’s spending.

“We’re going to focus on those who kept their promise to their constituents,” said Corry Bliss, who runs the group.

Veteran Republicans are sober about how daunting 2018 is shaping up to be, and hope that a clash on taxes at the very least offers the prospect of shifting the political debate onto more favorable terrain.

“If you’re a Republican and you think about what’s coming, and the range of things you could be fighting about, to have a fight about this tax bill is among the better things they can fight over in 2018,” said Bill McInturff, a G.O.P. pollster, conceding that Republicans are facing “very tough numbers.”

Mr. McInturff, who recently conducted a survey showing Republicans trailing Democrats by 12 points on the so-called generic ballot, said his party could not change the minds of those with fixed views about Mr. Trump, but that the tax bill offered an argument for those willing to hear them out.

“You better have something to say that the 60 percent is willing to listen to,” he said, noting polls that show 40 percent of voters want to impeach Mr. Trump.

Mr. Stivers acknowledged the partisan preferences of voters at the moment were tilting away from Republicans. “Right now there are people that don’t like the president, and they’re expressing it in that way,” he said of the generic ballot. But he suggested that voters uneasy with the president are still willing to support Republican congressional candidates, pointing to the Atlanta-area special House election the party won earlier this year despite a massive influx of money for the Democrats.

And he said he had urged his members to make taxes central. “Everybody needs to be talking about the tax bill, what it means for their communities,” said Mr. Stivers.

Democrats, though, said no piece of legislation could address the depth of the Republican challenge.

“It is unfixable,” said Anna Greenberg, a Democratic pollster. “And by November, tax reform could be a nonissue because what’s driving people to come out to vote is they don’t like the way the country is being run and the comportment of the president.”