Updated

Republican presidential candidate John McCain on Monday dismissed polls that show him slipping into single digits, arguing that his campaign is going through the typical ups and downs and will be fine this fall.

In an interview with The Associated Press, the Arizona senator also defended his support for a bipartisan immigration bill, a stance that has undercut his bid in early voting South Carolina.

The top Republican on the Senate Armed Services Committee acknowledged that his backing for the Iraq war has hurt his candidacy elsewhere in the country.

"I've got to do what's right," McCain told the AP. "In South Carolina, the war doesn't hurt me as much as in other parts of the country. It has hurt my candidacy."

McCain campaigned in South Carolina, which holds its GOP primary Feb. 2. He also raised money with Saturday's second-quarter deadline fast approaching and picked up the endorsement of Greenville, S.C., Mayor Knox White.

McCain spoke at two $500-a-person fundraisers in South Carolina. About 85 people turned out for the first stop in Columbia, S.C., while the second fundraiser in Greenville was later Monday evening.

A recent state poll showed McCain at just 7 percent in the race with top rivals Mitt Romney and Rudy Giuliani, and Fred Thompson close to announcing. A survey in Iowa also showed McCain in single digits.

"That poll is just not true," McCain said in the interview, referring to the South Carolina poll. With "veterans alone, we are doing much better than that."

In April, McCain overhauled his campaign operations after raising $12.5 million from January through March. That put him in third among Republicans, behind Romney and Giuliani. McCain didn't indicate whether the overhaul has helped him raise more money. However, more staff adjustments could be in the offing.

"I am totally confident that we'll have sufficient money to do what's necessary to wage a winning campaign," McCain said during a news conference.

In 2000, then-Texas Gov. George Bush's supporters here stopped McCain's momentum after he won New Hampshire. Seven years later, McCain now has the support of much of the GOP establishment that backed Bush.

"With the core support we have, we're going to do fine. We're going to do fine," McCain said in the interview, adding: "You watch in September."

With such a long campaign season, it was inevitable McCain would hit a slump, Knox said. But the mayor said he is backing McCain because he stands for what he believes in.

McCain "sometimes makes voters mad," Knox said. "They don't always agree with him. I don't always agree with him."