The political fallout from the partial government shutdown does not appear likely to affect the House Republicans who instigated it, given that so many of them come from deeply conservative districts where their constituents cheered the confrontation with President Obama.

But others in the GOP are worried.

Party veterans say they are increasingly concerned that a prolonged standoff in Washington could damage their prospects for winning back the Senate in 2014.

“You can see that in the different reaction of Senate Republicans” compared with their House counterparts, a prominent GOP pollster said.

Like several other Republican strategists interviewed for this article, he spoke on the condition of anonymity because he did not want to publicly disparage his party’s prospects or those of his clients.

See why some House Republicans might support a clean budget bill.

GOP senators — with a few notable exceptions, including and led by Ted Cruz (Tex.) — have been far more skeptical about the political wisdom of the shutdown engineered by House Republicans.

And now that it is underway, the party is looking for ways to distance its Senate candidates from the ensuing mess.

“It’s a referendum on Washington,” said Brad Dayspring, a spokesman for the National Republican Senatorial Committee. “Democrats have controlled Washington for the past five years.”

That, however, may be a harder argument to make for the seven GOP House members expected to seek Senate seats. All are in relatively conservative states, where the party believes it stands a good chance of winning next fall.

They include three candidates in a primary for the open Senate seat in Georgia: Reps. Paul C. Broun, Phil Gingrey and Jack Kingston.

In West Virginia, Rep. Shelley Moore Capito is considered a strong favorite to pick up an open seat, now held by Democrat John D. Rockefeller IV, for the Republicans.

Reps. Tom Cotton of Arkansas and Bill Cassidy of Louisiana are the Republican Party’s best hopes for beating vulnerable Democratic incumbents.

And in Montana, Rep. Steve Daines is expected to soon announce that he is running for the open seat that will result from a Democratic retirement.

All seven voted for a House bill that would fund the government, but only if the implementation of the new health-care law was delayed. The government shut down; the law went forward.

Even before the vote, GOP House members had not had such great luck lately in making the leap to the Senate.

Last year, five of them ran, and only one — Jeff Flake of Arizona — succeeded. Two former GOP House members, Peter Hoekstra of Michigan and Heather A. Wilson of New Mexico, also sought Senate seats in 2012 and lost.

By comparison, House Democrats were winners in four of the five Senate races in which they competed.

To regain a majority for the first time since 2007, Republicans would have to win six Senate seats — a big lift — but the electoral map gives them some advantages. Of the 35 states where Senate elections will be held, Democrats will be defending seats in 20, including in seven conservative states that were won by GOP nominee Mitt Romney in 2012. Of the 15 states where the Republicans are defending seats, Obama won only two, Maine and New Jersey. (New Jersey is in GOP hands because longtime Democratic incumbent Frank R. Lautenberg died in office, giving Gov. Chris Christie, a Republican, the opportunity to name a temporary replacement.)

The concern inside the party flows from the understanding that Senate races tend to be very different from House contests. Independent and swing voters have more influence in determining the outcome, even in states that are overwhelmingly red or blue.

The good news for Republicans is that independents generally agree with the GOP in their disapproval of the new health-care law, which is the signature achievement of the Obama presidency.

In the latest Washington Post-ABC News poll, 54 percent of independents expressed a negative opinion of the Affordable Care Act, while 42 percent had a positive view.

But the Republicans’ own numbers show that although independents do not favor the health-care law, they are even less enamored with the idea of shutting down the government to stop it.

The GOP super PAC Crossroads GPS recently conducted surveys in 10 states that are likely to have competitive Senate races, as well as in House districts that lean Republican or could go either way. It found that, among independents, 58 percent opposed shutting down the government as a means of stopping the implementation of the health-care law. Only 30 percent supported such a move.

Karl Rove, a Crossroads GPS founder and President George W. Bush’s top strategist, earlier cautioned Republicans that they were risking much if they pursued a government shutdown.

“Going down that road would strengthen the president while alienating independents. It is an ill-conceived tactic, and Republicans should reject it,” Rove wrote in the Wall Street Journal in mid-September.

The longer the shutdown goes on, Republicans predict, the more the blame will be spread around.

“It doesn’t help. We’re not going to vault up in the polls,” said Don Stewart, a spokesman for Sen. Mitch McConnell (R-Ky.), who not only is defending his seat next year, but also hopes to trade in his minority-leader title for that of majority leader.

But Stewart predicted that, ultimately, voters will decide: “In the government shutdown, it’s all D.C.”