(CNN) - Jeb Bush understands that as the son and brother of former presidents, his family name may hurt him as much as help him if he decides to run for the White House in 2016.
And the former two-term Florida governor reiterated that he'll make his decision on whether to launch a campaign for the Republican presidential nomination by the end of this year.
Bush, the featured guest Monday at the Long Island Association's biannual luncheon, a popular stop for former presidents and White House hopefuls, was asked about the recent comments from his mother. Former first lady Barbara Bush told CSPAN that "there's no question in my mind that Jeb is the best-qualified person to run for president, but I hope he won't," adding that "there are other families," who deserve a chance.
"It's an issue for sure," Bush admitted.
Bush told the story of sitting next to a man on a plane who talked about having a Bush and a Clinton and then a Bush in the White House, with the prospect of another Clinton and Bush to come.
Bush said "I get the point. It's something that, if I run, I would have to overcome that. And so will Hillary, by the way. Let's keep the same standards for everybody."
Former Secretary of State Hillary Clinton has said she'll decide by the end of the year if she makes another bid for the Democratic presidential nomination. Bush said that Clinton's decision would not impact his at all.
As for his timing, Bush said "that's a decision later on," adding once again that he'll decide by the end of the year.
Bush said that he's "old school" in that he feels that "one election should end before the next one starts," referring to this year's midterm elections. Bush said that he thinks a there's a lot that can be done in 2014 and that "I intend to campaign for a lot of candidates for my team, and I hope we can be victorious and I'd rather focus on that right now."
Bush is seen by many political handicappers as someone who could appeal to independents and moderates, as well as Hispanic voters, a demographic where thanks in part to the tough stance by many conservatives on immigration reform, Republicans have much work ahead of them.
"I think we've become a little more harsh than we need to be, so the first step would be to tone it down a bit, chill out," said Bush, adding that "we shouldn't be sending signals that turn them off from the get-go."
CNN Political Editor Paul Steinhauser contributed to this report.