Senate Republicans are warning that “Bush fatigue” could weigh on GOP chances of capturing the White House in 2016 if Jeb Bush wins the nomination.

Many Republicans think the former Florida governor would have made a better president than his brother George W. Bush, but GOP lawmakers now wonder if he has fallen out of step with the ideological direction of the party.

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More than seven years after leaving office, he’s struck a decidedly centrist tone which could make it hard to mobilize conservative base voters.

“It’s time to turn the page,” said Sen. Jim Inhofe (Okla.), a senior member of the GOP conference.

"Looking at it practically, there are others who could do a better job in terms of winning the election," he added. "It’s a little bit of Bush fatigue but the other thing is for a Republican to win a race like that ... you got to have someone who really engenders enthusiasm in the base. Jeb's a wonderful guy and all that, but I don’t believe he’d be able to do that."

Sen. John McCain (Ariz.), who was the party’s nominee in 2008, said Bush fatigue would be something to grapple with if he were the nominee, but that it wouldn’t necessarily sink Jeb’s campaign.

"I think it really is a factor, but so is the name ‘Clinton’ a factor," he said. "In some ways it energizes the vast Bush network. Then the unpopularity of George W. Bush is obviously a factor as well."

To current-day conservatives, the rise in government spending and debt during Bush’s eight years go against everything they believe. Their frustration peaked after the passage of the 2003 prescription drug act, which former Reagan policy adviser Bruce Bartlett called the largest expansion of the welfare state since Medicare’s creation.

Activists still grumble over President George H.W. Bush’s decision to raise taxes in 1990 after famously pledging, “Read my lips: no new taxes.” Grover Norquist, the president of Americans for Tax Reform, said it was the reason he lost his 1992 reelection campaign to Bill Clinton.

Jeb Bush hasn’t made a concerted effort to reach out to the growing wing of the party now, either -- he didn’t participate in the 2014 Conservative Political Action Conference and was left off its straw poll. And he stoked conservative ire when he declared earlier this week that immigrants who came to this country illegally “broke the law, but it’s not a felony. It’s an act of love.”

GOP senators praise Bush’s record in Florida, especially his accomplishments on education reform, but they are also eager to embrace a new generation of conservative leaders, represented by other likely presidential candidates Sens. Marco Rubio (R-Fla.), Rand Paul (R-Ky.) and Ted Cruz (R-Texas).

“I’m a Jeb Bush fan but I’m also a fan of turning over a new leaf, too,” said Sen. Jeff Flake (Ariz.), who in 2003 led a conservative revolt in the House of Representatives against the prescription drug bill.

Bush acknowledged recently that his family name could weigh on his campaign if he ran for president in two years.

"It's an issue for sure," Bush admitted in February during an event hosted by Long Island Association.

"I get the point. It's something that, if I run, I would have to overcome that. And so will Hillary, by the way. Let's keep the same standards for everybody," he said.

Bush’s mother, former first lady Barbara Bush told C-SPAN in a January interview that she hoped Jeb would not run for president.

"I think this is a great American country, great country, and if we can't find more than two or three families to run for high office, that's silly, because there are great governors and great eligible people to run," she said this year.

Jeb’s moves have become more visible in recent weeks as speculation mounts about a potential White House bid. He and other Republicans mulling presidential runs met with mega-donor Sheldon Adelson in March.

And he laid out his likely game plan on the campaign trail during a remarks this month at the George Bush Presidential Library and Museum, saying he will decide by the end of the year whether to run.

A spokeswoman for Bush declined to comment for this article.

GOP strategists say Bush would likely bid to become the candidate of the Republican, establishment but he has significant work to do before party lawmakers coalesce behind his campaign.

GOP senators had mixed reactions when asked about his possible candidacy.

“He would be a good candidate. I think it would be good for the party to have him in there,” said Sen. Rob Portman (R-Ohio), who served as White House budget director under George W. Bush.

But Portman stopped short of a ringing endorsement, noting that, “I’d be happy to see some of my colleagues run.”

Sen. Orrin Hatch (R-Utah) praised Bush as “a very, very strong candidate” and said the worry over Bush fatigue is overblown.

"If Hillary runs, they'd be hard-pressed to smear him because his last name is Bush," he said of Democratic strategists, noting that Clinton has to deal with the baggage of her husband’s administration

Hatch said he was also enthusiastic about Govs. Scott Walker (Wis.), Chris Christie and Bobby Jindal (La.) possibly running.

He paused and then added, “I think we’ve got some nice young guys too. I like Rubio very much. I like Rand Paul.”