Republican strategists expect Sarah Palin’s influence in midterm Senate races to diminish as the primary season concludes and GOP candidates turn their attention to winning over independents in the Nov. 2 general election.

The former Alaska governor and 2008 Republican vice presidential nominee is still projected to be a factor in a handful of races for the 11 Democratic-held Senate seats the GOP hopes to flip this fall. Republican operatives say few GOP campaign surrogates can match Palin’s fundraising prowess and ability to motivate the party faithful, and demand for her presence on the trail is likely to remain steady in some contests.

But with her approval ratings among independent voters at only 34 percent, according to the latest YouGov/Polimetrix public opinion poll, Palin could be less welcome in traditionally Democratic districts and swing states where a Republican candidate’s crossover appeal is crucial to victory.

Palin’s overall approval rating according to the Pollster.com average is 35 percent.

“She was a lot bigger draw in primary season than she will be during the general election,” a senior Republican Senate aide said Monday. “Nobody in the Republican Party can turn out the base like Sarah Palin, but the impression she leaves amongst independents is decidedly mixed.”

Sources say Palin has generally avoided direct collaboration with the Republican Party’s three Washington-based national campaign committees. But GOP strategists expect individual challenger and incumbent candidates to ask her for assistance. With 16 weeks until Election Day, requests for such help are likely to be increasingly strategic and localized — particularly among Senate candidates.

For example, should Dino Rossi win the Republican primary in Washington state, as expected, he wouldn’t want Palin to campaign for him in greater Seattle or the western half of the state generally. But he might find a Palin campaign appearance of value in conservative eastern Washington. Palin has in fact endorsed Rossi’s GOP primary opponent, Clint Didier. Rep. Mark Kirk (R), running for the Senate in Democratic-leaning Illinois, probably won’t ask for Palin’s help. But if he did, it might be to join him in conservative-leaning southern Illinois.

Former Hewlett Packard CEO Carly Fiorina, endorsed by Palin in the June 8 California GOP primary, probably will not ask Palin for further assistance as she seeks to oust Sen. Barbara Boxer (D) in the heavily Democratic Golden State. And former New Hampshire Attorney General Kelly Ayotte, the favorite in her state’s Senate Republican primary, is also unlikely to request help from Palin should she emerge as the GOP nominee.

But Rep. John Boozman (R), hoping to upend Sen. Blanche Lincoln (D) in culturally conservative Arkansas, probably will. Meanwhile, Sen. John McCain (R-Ariz.), already endorsed by Palin in his intraparty battle with former Rep. J.D. Hayworth, a darling of many conservatives, might ask his former presidential running mate for more help in the general election campaign if he wins his Aug. 24 primary.

“It depends on how active the tea party or even the Ron Paul types are in the state,” said one Washington-based Republican operative. “She will be asked for, but for only those races where she helps — and that’s certainly not Republicans across the board.”

An attempt to reach representatives of Palin for this story was unsuccessful.

Palin in most cases appears to have acted independently and outside of the traditional Republican Party structure when it came to deciding whom to back and how much of her muscle to lend to a campaign. In fact, it’s Palin’s anti-establishment seal of approval that has made her endorsement so valuable throughout this election cycle.

Palin has backed the anti-establishment primary candidate for Senate in at least four cases, including endorsing Joe Miller, who is challenging GOP Conference Vice Chairwoman Lisa Murkowski in Alaska, raising concerns among some Republicans that she might cost her party seats in some cases if she succeeds in nominating candidates with little chance of winning in the general election. But Republican strategists inside the Beltway still rate her activity in GOP Senate primaries as positive overall. In House races Palin has played in, GOP operatives tend to describe her effect on Republican candidates as overwhelmingly positive.

In already-concluded Senate GOP primaries, Palin backed Sharron Angle, who is challenging Majority Leader Harry Reid (D-Nev.), and Rand Paul, who is running for an open seat in Kentucky and defeated Minority Leader Mitch McConnell’s (R-Ky.) favored GOP primary candidate. Palin also has endorsed Didier, a former professional football player and tea party activist, in the upcoming Washington state GOP primary — while national Republicans are backing Rossi.

But Palin’s moves have been unpredictable. She has done little for Didier beyond promoting him on Facebook and Twitter. And her endorsements of Fiorina and McCain — two candidates in need of strengthening their right flanks — disappointed conservative activists.

Senate Minority Whip Jon Kyl (R-Ariz.) said Palin’s endorsement was very helpful to McCain, the 2008 GOP presidential nominee who in recent years has found himself the target of conservatives unappreciative of his willingness to compromise with Democrats on major legislation. Perhaps because of pressure from Hayworth, McCain’s bipartisanship has been less on display this cycle.

“I know he appreciated [her endorsement], and she has a strong following in Arizona, so I’m sure that was helpful,” Kyl said.