A third Bush fighting for the presidency in 2016 looks a serious possibility as Jeb emerges as Republican candidate

Those against the Tea Party right have increasingly come to view the 61-year-old as the only person capable of waging a credible campaign

Jeb Bush says he spends every day trying not to think about whether to run for the presidency (Getty Images)

Jeb Bush has admitted in the clearest terms yet that he is thinking seriously about running for the Republican nomination for president in 2016 by telling an audience in Texas that he is trying not to.

The former two-times governor of Florida and brother and son of former presidents said his reluctance to get too deep into the question now means a decision is not imminent. But he won’t leave the party hanging forever. “I’ll make up my mind [by] the end of the year… I just don’t want to go through that until the right time,” he said, adding that he spends “every day trying to avoid having to think about it”.

Traditional Republicans – as against the Tea Party right – have increasingly come to view Mr Bush, 61, as the only person capable of waging a credible campaign in 2016, particularly if Hillary Clinton emerges as the Democrat nominee. His role as a potential saviour has come into focus in part because of the George Washington Bridge lane-closure scandal that has enveloped New Jersey Governor Chris Christie.

But in speaking on Sunday night to an audience gathered at the George W Bush Presidential Library in Dallas to mark the 25th anniversary of the presidency of George HW Bush, his father, the former governor also managed to demonstrate why his running for the White House might just as easily cleave the party in two as reunite it, with comments on education and immigration that would inflame Tea Party activists. The reasons for Mr Bush to decline are many, including his home life. “Is it OK for my family?” he asked. “Is it something that is a huge sacrifice for my family?”

Running would open his Mexican-born wife and their children to intense scrutiny. One daughter has had tangles with the law over drug use. His son George P Bush is beginning a political career of his own in Texas and might not want his father taking his oxygen. There is also the problem of his name. A recent ABC/Washington Post poll showed that 50 per cent of Americans would not be ready to vote for yet another Bush.

It is 12 years since he last ran for election, in Florida, and he signalled his distaste for the attack-ad negativity of national campaigns today. “Can a candidate run with a hopeful, optimistic message, hopefully with enough detail to give a sense that it’s not just idle words and not get back into the vortex of the mud fight?” he asked.

On immigration, he almost set up the mud fight even before declaring by saying that some of those who enter the US do so out “of an act of love”, coming often for family reasons. That implies both joining family members already in the US and remitting money they earn to families back home. Such sentiments are anathema to the party’s right.

“Yes, they broke the law, but it’s not a felony,” said Mr Bush, who is fluent in Spanish. “It’s an act of love. It’s an act of commitment to your family. I honestly think that that is a different kind of crime, that there should be a price paid, but it shouldn’t rile people up that people are actually coming to this country to provide for their families.”

Though Mr Bush has solid conservative credentials, he would be pegged as the moderate in a primary battle for the nomination. His biggest problem would be that the voices of independent and moderate voters tend to be overwhelmed in early primary votes by the more conservative forces.

In Dallas, Mr Bush repeated his support for national school standards, the Common Core, which used to have wide party support until the Tea Party declared its opposition. “I just don’t seem compelled to run for cover when I think this is the right thing to do for our country,” he said. “And others have, others that supported the standards all of a sudden now are opposed to it. I don’t get it. High standards matter.”