(Updated 7 p.m.) In his pitch to a labor convention, Chris Murphy, who is likely to walk away with the group’s endorsement in the U.S. Senate race, ignored his Democratic opponent in the primary and went after his potential Republican rival, Linda McMahon.

He was the latest office-seeker to address the statewide labor group, which is holding its convention in Hartford this week.

“The contrast in this race involves a bright line that exists nowhere else in this country,” Murphy told the AFL-CIO convention. “Now I don’t begrudge the fact that Linda McMahon has made a billion dollars in her lifetime. But the question is this: If her first success in her first career came by creating dangerous working conditions, denying her employees health care, and shipping jobs overseas. Why on earth would we expect her to suddenly change her tactics in her second career?”

McMahon was the CEO of World Wrestling Entertainment. She stepped down in 2010 during her first run for U.S. Senate.

Erin Isaac, McMahon’s campaign spokeswoman, fired back:

“Washington’s assault on the private sector has got to stop,” Isaac said. “Congressman Murphy has been in elected office for a dozen years and still has no idea how to create a single job. As a matter of fact Connecticut is actually 62,000 jobs in the hole thanks to the policies he has championed since taking office.”

But job creation aside, Murphy has to beat former Secretary of the State Susan Bysiewicz before he even gets a shot at McMahon, who is facing her own challenge from former U.S. Rep. Chris Shays. Shays will address the convention at 9:30 a.m. Tuesday.

Murphy said he’s not taking the Democratic primary against Bysiewicz for granted, but Monday was his one chance to address the differences between him and McMahon to the all union crowd

“Linda McMahon’s money doesn’t allow me to just talk about the primary, then in late August focus on the general election,” Murphy told reporters after his pitch. “I’m thrilled I have a big lead in the primary, but I’m not taking it for granted.”

Bysiewicz addressed the coalition of unions earlier in the morning and continued to tout her stance against Wall Street using Murphy’s one 2010 vote on an omnibus bill to paint him as someone who doesn’t support working families.

The bill Bysiewicz was referring to was the 433-page American Jobs and Closing Tax Loopholes Act , which primarily extended unemployment compensation before being amended to offer tax breaks to specific populations. It changes the tax treatment of carried interest which is the main source of income for hedge fund managers.

For the past two years she’s been throwing the same punch and it’s not sticking, Murphy said of Bysiewicz’s attack.

“People don’t believe what she’s saying. I’ve voted for tax fairness my entire career,” he added.

The latest Quinnipiac University poll shows Murphy leading McMahon by three points in the general election, but his statewide name recognition remains low. The June 6 poll showed about 46 percent of voters polled haven’t heard enough about him to form an opinion.

“I’ve got a challenge ahead of me. I’m going to run one-fifth the number of TV commercials,” Murphy said.

He said that makes an endorsement from the AFL-CIO all the more important because it means volunteer support.

“It’s the people in that room that are going to have to be my TV commercials,” Murphy said. “Hard work is going to have to be a substitute with money when it comes to my campaign.”

Murphy has already received endorsements from some of the various constituent unions of the AFL-CIO, including the Connecticut Fire Fighters, United Auto Workers, Connecticut Laborers, the Connecticut State Building and Construction Trades Council, and the Communications Workers of America.

McMahon addressed the labor convention earlier in the day. Read more about her pitch here.