With a few hundred thousand dollars in his campaign coffers, former U.S. Rep. Chris Shays hopes next month’s Republican U.S. Senate primary will not be determined by how much money his Republican rival, Linda McMahon, spends.

McMahon—who spent an unprecedented $50 million of her own money in an unsuccessful bid for U.S. Senate two years ago—is again writing big checks to her campaign, but Shays believes right now Aug. 14 primary race is “a dead heat.”

“If I had $500,000 more money, I wouldn’t even wonder who would win this primary,” Shays, who represented the 4th District for 21 years, said last week while touring diners and restaurants between Danbury and Southbury.

“It’s not what she has, it’s what I have,” he said.

Former state Sen. Sam Caligiuri, R-Waterbury, a Shays supporter, agrees.

“If he has enough resources to get out his message of what he accomplished in Congress and his plan to revive the economy, he can win,” he said. “Linda has high unfavorable ratings in the polls, which mystifies me because she is so likeable and is such a dynamic speaker. But that continues to be the case.”

Shays raised $530,000 during the quarter that ended last month, which is his best take to date, but he is still well behind the other three candidates in the race for the seat that is being vacated by four-term U.S. Sen. Joe Lieberman.

Democratic U.S. Rep. Chris Murphy has raised $5.5 million, including more than $1.2 million in the most recent quarter. Former Secretary of the State Susan Bysiewicz raised about $2.25 million, including more than $355,000 this quarter.

McMahon has loaned her campaign millions of dollars, but unlike 2010 the former CEO of World Wrestling Entertainment is also raising small donations from supporters. McMahon’s campaign plans to release its numbers today. Her campaign said Saturday that it received contributions from 1,500 new supporters during the latest quarter.

Shays, who didn’t enter the race until last October, has collected about $1.4 million, loaned his campaign $100,000 and has about $327,000 on hand for the primary.

It means he doesn’t have enough money to air television commercials, which is bad news for a candidate who 44 percent of voters surveyed in June didn’t know enough about to even form an opinion.

“She’s doing better in the polls,” Shays admitted of McMahon. “The question is: Do her people come out or do my people come out?”

Tim Quinn, a spokesman for Shays, said based on recent results they expect about 150,000 Republicans to vote in the primary, but that could be optimistic since about 124,000 Republicans turned out in 2010 two years ago for what was a three-way primary.

But Shays, who has won tough primary battles against self-funded candidates in the past, is not discouraged.

Shays said he has been receiving a favorable response from voters over the recent weeks at public events and retail outlets. He said voters are concerned about the sexually-explicit content that McMahon broadcast on WWE and her lack of knowledge on policy issues nearly three years after she first ran for the U.S. Senate.

Through the Republican state convention in May, his strongest argument for winning the nomination was polls that showed he was more competitive than McMahon against Murphy, but he lost that argument in the most recent June poll which showed him trailing both McMahon and Murphy.

A Quinnipiac poll in March reported that Shays trailed Murphy just 41 to 40, while Murphy was ahead of McMahon 52 to 37 percent.

However, the June poll indicated that Murphy now led Shays 45 to 37 percent, while McMahon now trailed Murphy just 46 to 43 percent.

In the Republican primary, the March Quinnipiac poll showed McMahon leading Shays 51 to 42 percent. But McMahon led 59 to 30 percent in a poll taken last month. Some McMahon supporters have suggested that Shays withdraw to give the GOP and edge entering the general election campaign.

“That’s pretty artificial,” Shays said of the result from the most recent poll. “She spent $2 million on television commercials right after the convention without any counterbalance from our campaign.”

“It’s not insignificant,” he said of the poll. “But it’s just a moment in time.”

Unlike the other three candidates Shays has not aired any television commercials and doesn’t plan to do so before the primary.

McMahon, who received several early endorsements from state GOP leaders, took 60 percent of the delegates at the state convention in May to 32 percent for Shays, who didn’t enter the race until last October after completing work as the co-chairman of the federal Commission on Wartime Contracting.

Shays said the loss at the convention and the recent poll results have not diminished the enthusiasm of his campaign team.

He said his headquarters in Stratford is full of volunteers, who are making 2,000 to 3,000 calls each night and also canvassing door-to-door throughout the state.

However, in contrast, Tim Murtaugh, McMahon’s communications director, said her campaign has mounted an ambitious voter outreach since the convention. He said McMahon now has eight offices and that from June 1 through July 11 her volunteers contacted a combined 156,000 voters by phone or going door-to-door. On Saturday McMahon’s campaign showcased their grassroots efforts by contacting more than 38,000 voters in one day. Volunteers at eight different offices around the state made phone calls to Republicans and unaffiliated voters, in addition to knocking on doors.

Republicans have not won a U.S. Senate race in Connecticut since 1982, when Lowell Weicker captured a third term. Two years ago, McMahon lost by 12 points to Democrat Richard Blumenthal of Greenwich.

The 5th District, which stretches through the western part of the state from Newtown to Salisbury, is where McMahon did her best among the state’s five congressional districts, losing to Blumenthal by just 2,043 votes.

State Rep. Dan Carter, R-Bethel, said the Danbury area appears to be up for grabs.

“Personal contact means a lot,” he said. “Linda McMahon has spent a lot of time here and Chris Shays has spent a lot of time out here.”

Carter said he endorsed McMahon last year before Shays entered the race.

“Once I endorse, I don’t flip,” he said as Shays greeted voters at the New Colony Diner in Bethel. “But Chris is a dear friend, and I hope he gets a shot at this.”

How well Shays does may depend on how he does during the last televised debate before the primary. Shays and McMahon will meet for a debate 7 p.m. Wednesday, July 18 on NBC Connecticut.