But President Bush did so when the federal budget looked flush and it was politically possible to offer a deficit-increasing tax cut. Budget deficits have required Republican candidates to propose at least partial offsets to their tax rate cuts, which led to Mr. Romney’s problem of having to explain whose taxes he would raise.

Gov. Chris Christie, who is not yet a candidate but sometimes acts like one, gave a speech in New Hampshire last week in which he called for a tax plan similar to the one Mr. Romney ran on three years ago. He was, however, looser with the specifications, which could help him avoid the accusation of raising taxes.

Mr. Christie eased off Mr. Romney’s revenue neutrality pledge, saying his plan would not “materially increase the deficit” after combining with other measures. That would leave himself room to pay for tax cuts with spending cuts, allow for a small deficit increase and avoid the implication that anyone’s taxes would have to go up.

Similarly, Senator Marco Rubio has endorsed a plan that tosses aside any commitment to revenue neutrality. It would reduce revenue by trillions of dollars over a decade by cutting rates, abolishing taxes on capital gains and dividends and creating a new tax preference for business owners. Mr. Rubio told reporters in March, “I’ve never believed that tax reform by itself should pay for itself.”

Scott Walker, the governor of Wisconsin who has yet to declare himself a candidate, has not spoken out in detail on federal tax issues. In March, The Weekly Standard quoted him saying: “I like the idea of a more fair and simple tax code.”

The one who seems to have taken the Romney tax trap lesson most to heart is Jeb Bush, who has so far said nothing specific about what he would do on taxes.

“I think we need to cut taxes and reform our code to create economic prosperity,” he said in an interview with National Review’s Rich Lowry in April. Unusually for a Republican, he has said he will not sign the Americans for Tax Reform pledge not to raise taxes. (In 2012, all major Republican presidential candidates signed the pledge except Jon Huntsman.) He has responded to specific questions about what he would do on taxes as president by talking up his tax-cutting record as governor of Florida, not by making any promises.

Given his family history with “Read my lips, no new taxes,” it’s no surprise Mr. Bush would be hesitant about tax promises. The question is whether G.O.P. primary voters, used to promises of deep tax cuts, yet desirous of higher military spending and wary of old-age entitlement cuts, will allow a candidate to dance around their unreasonable expectations — or whether they will push their nominee into promises that prove unpopular in a general election.