Mr Bush, Governor of Texas, has assembled a Presidential Exploratory Committee that is more diverse and open than any of his opponents. He presented himself as the heir to the party of Reagan and Lincoln at a time when it is increasingly seen as right-wing, exclusive, rich, white and Southern, and obsessed with toppling Bill Clinton rather than policy.
"I want the party of Lincoln to be the party that makes sure no one is left behind," said Mr Bush in Austin, the Texas state capital.
"Ours is a party that is open, that is diverse, that is principled." The party had tended to ignore minorities, especially the Hispanic community, he said.
Mr Bush, 52, is sometimes referred to as just "Dubya" to distinguish him from his father, the former President. He calls himself a "compassionate conservative", to distinguish himself from the party's ideological right wing.
He had confirmed earlier in the week that he would form a Presidential Exploratory Committee. If he wins the Republican nomination, then he will probably face Al Gore, the US Vice-President and most likely Democratic candidate in 2000.
The evidence from his selection of advisers is that he is actively courting just about every possible constituency in America. J C Watts, the only black Republican in the Congress, was on the 10-person team, with Henry Bonilla, the first Republican Hispanic to be elected to Congress from Texas. There are three women: Jennifer Dunn from Washington, the first woman of either party to run for Majority Leader in the House of Representatives, Ann Northup from Kentucky, and Condoleeza Rice, a former White House official.
He has also diversified his team regionally. There is a Mid-Westerner, Michigan Governor John Engler, a Southerner, Republican Senator Paul Coverdale from Georgia, and Roy Blount from the Plains state of Missouri. Haley Barbour, former Republican Chairman, brings considerable fund- raising expertise and George Shultz, former Secretary of State and of the Treasury, lends gravitas and experience.
Mr Bush spent much of the weekend speaking to the Second Baptist Church in Houston, Texas's largest church and one of the biggest in the country. Securing the support of the religious right will be crucial to his campaign.
He has also been assisted by Ralph Reed, the highly influential former executive director of the Christian Coalition, in making connections in North Carolina. That is the home state of Elizabeth Dole, Mr Bush's chief opponent for the Republican candidacy.
Mr Bush will not formally declare his candidacy until June, after the state legislature has finished its business. But he left no doubt of his intentions. He talked about "when I leave Texas next June". And when asked about comparisons with his father, he said: "He is not the candidate. I am the candidate," later correcting himself.