"I have enough self-awareness to know that this is the bumpy time of a campaign," he said on NBC's "Meet the Press."
Bush, brother and son of former presidents and ex-governor of Florida, was once considered the man to beat in the nomination race for the 2016 election.
But his campaign has floundered, in particular last week when he seemingly bombed out in the latest Republican debate among the crowded field of candidates.
He flubbed badly on national television while trying to attack Senator Marco Rubio, a political protege and fellow candidate, for missing Senate votes while campaigning.
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"This is the process. I totally understand it, and I'm more than prepared to fight on," Bush said in the interview aired today.
He also acknowledged that he has to get better as the debate season continues.
"I am a grinder. When I see I'm not doing something well then I reset and get better," he added.
Weighing in on another issue, Bush said he felt torn by the death penalty.
He said his Christian faith urges him to be against it, but that he also understands the pain of victims of violent crime and their need for justice and what he called closure.
"We should reform it. If it's to be used as a deterrent, it has to be reformed," Bush said, referring to the years death row inmates spend mired in the appeals process waiting to know their fate.
"It can't take 25 years, that does no one any good. Neither the victims nor the state is solving this problem with that kind of tangled judicial process.