The Democratic Party of Tennessee has accused Thompson of using his homestate as "his personal ATM." Thompson also spent three days last week fundraising in Texas.
Reed said Thompson's fundraising push shows he lacks a national financial structure.
"If you look at what he's doing in fundraisers this week, he's doing Tennessee," Reed said. "That isn't exactly a knock'em, rock'em, sock'em roll out of fundraising. You'd think he'd be doing New York, Chicago, Miami, L.A., Dallas."
Another campaign to watch is Sen. John McCain, R-Ariz., who has battled severe campaign financial woes and staffing shakeups.
In the second quarter, McCain's campaign raised about $11.6 million, but spent almost $13.1 million.
However, those close to his campaign argue that things are turning around.
"We're in the black," said Republican strategist Charlie Black, a chief advisor to McCain's campaign. "In each of the months of this quarter, we've taken in more money than we've spent."
"The important thing is not so much our fundraising, but our budget," McCain told reporters in Concord, N.H. on Sept. 4. "Thank God, we have reduced our budget dramatically, and that's the important thing, the expenditures."
However Republican strategists argue that may not be enough of a turn around to get McCain's campaign into front runner status.
"Without the donors, you are nothing," said Sheri Annis, a former Republican strategist. "You're only as powerful and as credible as your finances and therefore the media allow you to be." she said.
Annis also said that Gov. Mike Huckabee, R-Ark., who had a strong showing at the Iowa Straw Poll, needs to have a strong third quarter fundraising report.
"He has to show that he has more than just organizational skills in one place," Annis said.
Former Gov. Mitt Romney, R-Mass, was the GOP fundraising leader in the first quarter, however former Mayor Rudy Giuliani, R-N.Y., inched ahead during the second quarter -- and Romney topped off his campaign war chest with his own personal wealth to stay competitive.
The Romney campaign wouldn't say whether or not their candidate would write himself a check this time, but a Romney aide suggested Giuliani's fundraising capability is explainable by his national name recognition.
Romney's campaign is also lowering expectations this week.
"This quarter is a challenge, because the summer months are a slower time for fundraising," said Romney campaign spokesman Kevin Madden.
On Friday, the Romney campaign will hold a rally in Salt Lake City, Utah.
"We've put a premium on growing the number of new donors, so we can continue to work with them as we build our national grassroots organization," he said.
GOP strategists said Republicans are watching not only who is leading the field when it comes to fundraising, but who is also spending the most money.
"Romney's the guy to watch on that," Reed said, suggesting Romney is spending his money faster than the other candidates. "It's not just how much people are raising -- it's their burn rate and how fast they're spending their money."
ABC News' Bret Hovell, Jonathan Greenberger, Christine Byun, Jan Simmonds and Rick Klein contributed to this report.