But in ways big and small, deliberate or subconscious, the younger Mr. Bush seems to have defined himself as the anti-George W. Bush: an intellectual in search of new ideas, a serial consulter of outsiders who relishes animated debate and a probing manager who eagerly burrows into the bureaucratic details.

Allies said that reputation — as what the Republican strategist Karl Rove called the “deepest thinker on our side” — could prove vital in selling Mr. Bush as a presidential candidate to an electorate still scarred by George W. Bush’s legacy of costly wars abroad and economic meltdown at home.

But the bookishness and pragmatism that strike mainstream Republican leaders as virtues highlight the potential difficulty that Mr. Bush may face in igniting the passions of more conservative members of the party.

The questions he grapples with most frequently, and enthusiastically, revolve around improving the effectiveness of government in areas like education, immigration and criminal justice. It is a message unlikely to electrify Tea Party and libertarian wings of his party that are openly hostile to the very idea of government.