Washington CNN —  

Former Florida Gov. Jeb Bush will not sign a pledge promising not to raise taxes, or any pledges from “lobbying groups,” a spokeswoman said this weekend.

“If Governor Bush decides to move forward, he will not sign any pledges circulated by lobbying groups,” spokeswoman Kristy Campbell said in a statement. “His record on tax cuts is clear. He didn’t raise taxes.”

His refusal comes in response to a call from Grover Norquist, head of the anti-tax group Americans for Tax Reform, to sign his Taxpayers Protection Pledge, in which candidates commit to opposing tax increases.

The issue of taxes could hang over Bush’s presidential bid, if he runs, as his father was famous for the strident campaign pledge — declaring, “read my lips: no new taxes” — that he broke.

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Norquist suggested Bush may go the way of his father in a tweet.

“If my dad threw away a perfectly good presidency I would honor him by learning to avoid that mistake,” he tweeted.

“Most pledge takers keep the pledge,” Norquist added in a later tweet. “Those who refuse to sign all raise taxes when pushed hard enough by spenders.”

But Campbell defended Bush’s record on taxes.

“He cut them every year as governor for a total of more than $19 billion in tax relief. He does not support raising taxes and believes cutting taxes and reforming the tax code will lead to greater economic growth and more prosperity for Americans.”

Bush has not yet officially announced plans to run for president, but he’s been building an operation and visiting early primary states in preparation for a likely run.

CNN’s Ashley Killough contributed to this report.