Bush, the brother of President George W Bush and son of President George Bush Sr, is a beloved figure among many conservatives who see him as a strong and charismatic leader who is popular in the must-win swing state of Florida.
That contrasts with a widespread unease among many Republican leaders and grassroots activists with the remaining crop of Republican candidates and the vitriolic nature of the fight between frontrunner Mitt Romney and his main challengers Rick Santorum and Newt Gingrich.
In answers to questions from the audience after a speech in Dallas on Thursday, Bush cautioned the remaining Republican campaigns from drifting so far to the right that they put off the key independent voters needed to beat President Barack Obama in November.
"I think it's important for the candidates to recognise though they have to appeal to primary voters, and not turn off independent voters that will be part of a winning coalition," Bush told the audience according to CBS news.
Bush also directly took on the strident tone of recent Republican debates, accusing participants of scare-mongering rather than trying to get them to look over the horizon for a broader perspective.
With Mitt Romney failing so far to secure the nomination but with no convincing challenger emerging to unseat him, many Republican pundits have speculated about the possibility that none of the current field will be able to amass enough support to secure the nomination this August in Tampa without an old-fashioned contested convention.




