If money is what really matters in politics, the Republican presidential contest is already a two-man race.

Rick Perry and Mitt Romney are sitting on four times as much cash as the rest of the GOP field combined, giving them a commanding edge in resources in the final weeks before Republican voters begin casting ballots, according to new campaign disclosure reports.

Other GOP hopefuls, such as the surging Herman Cain, argue that a strong message that resonates with grass-roots voters will propel them to victory, with or without hefty campaign treasuries. But history suggests that presidential nominations are ultimately won by organization, media exposure and lots of face time with voters — all of which cost plenty of money.

Romney has raised more than $32 million so far this year and still has about half that much in the bank to help pay for staff, grass-roots organizing and television ads in New Hampshire, Iowa and other early-voting states. Perry, meanwhile, raised money at the rate of $2.5 million a week after his splashy entrance into the campaign, giving him even more cash on hand than Romney at the close of last month.

Their financial dominance gives Perry and Romney a significant leg up as they attempt to overcome steep challenges in the weeks ahead. For Romney, that means breaking through a ceiling of support that has kept him stalled for months at about 25 percent in national and state polls as GOP primary voters flirt with a shifting list of alternatives.

And for Perry, the money gives him a fighting chance to reverse a disastrous slide in popularity in recent weeks. After a barnstorming start in which he overtook Romney, the Texas governor’s standing plummeted with a series of weak debate performances and his defense of a tuition program for children of illegal immigrants that angered many conservatives.

“Fundraising is obviously an important part of the campaign process. It allows you to run a competitive campaign,” said Perry spokesman Mark Miner. “This race is going to be won in the states during these early primaries. That’s where our focus is going to be. The goal is to use all available resources to win.”

Others in the GOP field, however, note that the race is still volatile and insist that a strong message and enthusiastic grass-roots support will enable them to compete. Both Perry and Romney rely heavily on deep-pocketed donors who give up to the $2,500 maximum under federal election rules, with relatively few contributors giving $200 or less. They also have the benefit of well-funded “super PACs” founded by some of their closest aides that can raise and spend unlimited funds to help them win the nomination.

Cain, a former pizza executive who has vaulted to the top of recent polls, said this weekend that “money isn’t what’s driving my momentum — my message is driving my momentum.”

“When you hear about all of the money that’s being raised by other candidates, and this Cain campaign has a measly million dollars in available funds, do not fret, my friends,” the candidate said at a fundraiser in Cookeville, Tenn., on Saturday. “Because message is more powerful than money, because of you, the people.”

New disclosure reports show that Cain has a long way to go financially with just $1.3 million in the bank and nearly $700,000 in debt at the end of last month. But Cain also says his campaign has raised an additional $2 million over the past two weeks. “Our fundraising is now beginning to pick up,” he said Sunday on NBC’s “Meet the Press.”

Perry, who didn’t begin his campaign until mid-August, raised $17.2 million through September and still had $15.1 million in the bank, records show. Romney had $14.7 million on hand Sept. 30 despite spending nearly that much in the third quarter.

“We’re extremely proud of the $32 million we’ve been able to raise thus far,” said Romney spokeswoman Andrea Saul. “We will have the resources we need to compete in all 50 states and educate voters about Gov. Romney’s plan to create jobs and revive this economy.”

Others lagged far behind. Rep. Ron Paul (R-Tex.) had $3.6 million on hand, while Rep. Michele Bachmann (R-Minn.) had $1.5 million. Two candidates — former House speaker Newt Gingrich and former U.S. ambassador to China Jon Huntsman Jr. — were deeply in debt with almost no cash left.

And none of the Republicans have come close to President Obama, who has raised more than $90 million for his campaign and $65 million for the Democratic National Committee.

Political scientists argue fiercely over the role of money in politics, and there are numerous cases of well-funded tycoons going down to defeat in a general election. But many academics and political strategists agree that money can play a particularly crucial role in party primaries, where even a small edge in spending can have an enormous impact.

In one recent paper examining the 2008 primaries, Dino P. Christenson of Boston University and Corwin D. Smidt of Michigan State University noted the rapid rise and fall of GOP long shot Mike Huckabee, whose campaign quickly deflated after his Iowa caucus victory because he did not have the resources to compete in subsequent contests.

What’s more, they said, fundraising success begets even more fundraising, as major donors and party activists flock to candidates who show the ability to attract financial support.

“It is unclear how much of a causal influence money has on nomination victories, but it is generally accepted that having large sums of money is a necessary component for candidates to compete and win their party’s presidential nomination,” the researchers wrote.

The underfunded candidates in the 2012 field remain unbowed. Alice Stewart, a spokeswoman for Bachmann, said the Minnesota congresswoman will focus on “connecting with people one-on-one” in neighboring Iowa, where she was born and where caucus-goers have often rallied to the underdog.

“Our plan is to execute the same strategy that led us to victory at the Iowa straw poll” in August, Stewart said. “With the foundation we have already in place, we are confident we can win the Iowa caucuses and carry that momentum to success in South Carolina and the other early states.”

Some political strategists agree that the race remains too unsettled to call based on who has the most money. Mark McKinnon, a former campaign adviser to George W. Bush and Sen. John McCain (R-Ariz.), said the importance of fundraising is “way overblown.”

“Message and momentum can make up for lack of funds,” McKinnon wrote in an e-mail Sunday. “Right now Herman Cain has two out of three. I wouldn’t count him out.”

Dive into the campaign finance tracker with our new Campaign Finance Explorer.

Staff writers T.W. Farnam in Washington and Sandhya Somashekhar in Cookeville contributed to this report.

Read more on PostPolitics.com

Can Obama hold on in the South?

Cain: Some would pay more under ‘9-9-9’ plan

Fact Checker: Axelrod’s spin gets ahead of the facts

Rick Perry’s war on drug cartels