Thompson is looking to beat fellow Republicans and current front runners Massachusetts Gov. Mitt Romney, Arizona Sen. John McCain and former New York City Mayor Rudy Giuliani.
"I am a long shot but the truth of the matter is nobody is really able to maintain the lead on the Republican side, it's wide open," Thompson told Milwaukee's TMJ4 television station Tuesday. "Why not somebody from the upper Midwest, somebody with work ethics and the ideals and ideas that's going to make America better?"
On Wednesday, Thompson spoke first at Messmer High School in Milwaukee, a Catholic school that participates in the voucher program he created as governor, which allows low-income families to send their children to private schools at state expense. He said that he would push for a similar nationwide voucher program as president.
Thompson then continued to Clive, Iowa for a noon event. He has been focusing his campaign strategy in Iowa, which holds the nation's first presidential caucuses, by making weekly visits to the state since forming his presidential exploratory committee in December.
Thompson, a four-term Wisconsin governor and the health and human services secretary during President Bush's first term, originally confirmed his candidacy Sunday during an interview on ABC's "This Week."
"I am the reliable conservative," he told ABC's George Stephanopoulos.
On the program, Thompson said that his Iraq policy would differ from President Bush's policy. He outlined a three-part plan that included a vote by Iraqi legislators on continued U.S. presence in the country; local elections in Iraq's 18 provinces; and a new, equal division of oil revenues between the Iraqi federal government, provincial governments and individual citizens.
Thompson also said he disagreed with the Democratic Congress' recent bill to set a timeline for withdrawing U.S. troops, saying that the measure would send a message to U.S. enemies that "we are not there for the long haul."
While Thompson lags behind other Republican contenders, many GOP voters have not yet chosen who to support, so the door is not closed on candidates who are not in the top three, University of Iowa pollster and political scientist David Redlawsk told Congressional Quarterly.
"Consequently we think there actually is still an opening in the Iowa caucus for potentially other candidates on the Republican side," he told the paper.