"My zip code is 78701. That's Austin, Texas. It's not Washington, DC. I'm not part of the Washington scene," Bush told CBS News' Face The Nation in Bedford, N.H. on Sunday.
"I don't want anybody in this state to think I'm taking anything for granted, because I'm not," he added about his chances in Tuesday's presidential primary.
In the latest public opinion polls, Bush and his rival, Arizona Senator John McCain, are in a statistical dead heat in the GOP race in the Granite State. During the campaign so far, Bush and McCain have clashed sharply over tax cuts. McCain has criticized the Texas governor's $483 million tax cut plan as too large and favoring the wealthy.
Bush told Face the Nation that McCain believes like the Clinton Administration that a tax cut should be "something significantly less" than what his plan offers.
"John McCain believes we ought to leave the money in Washington. I don't," he said.
Still, Bush found a few kind words for his rival as the New Hampshire race draws to a close - saying he would never compare him to President Clinton when it came to character.
"John McCain is a man of enormous character. And he was a friend of mine before this campaign. He will be a friend of mine after this campaign," said Bush.
On abortion, the Texas Governor attempted to crawl back towards the political center on the issue after recent tugs to the right by his GOP rivals.
"It's an important issue, but not the only issue," Bush said. "It is important to have a president explain the value of life."
Bush has said he will not use abortion as a litmus test to pick a running mate or choose Supreme Court justices. But last weekend, Bush toughened his anti-abortion tone on the eve of the Iowa caucuses amid attacks by GOP rival Steve Forbes that he was a "pro-life pacifist." That's when Bush blasted the Supreme Court's landmark Roe vs. Wade decision as "flawed" and stressed he would appoint only "strict constructionists" to the nation's highest court.
But on Sunday, Bush said "I know I'm a uniter, not a divider. I'm confident I can help the country come up with common ground to help reduce the number of abortionsWe ought to have the goal that says children unborn and born ought to be protected in law and welcomed in life,"
And on gun control, Bush called President Clinton's idea for states to issue handgun licenses similar to driver's licenses "a reach" that isn't going to happen.
"I think instant background checks and enforcing laws would" have more of a real impact, Bush said.