Connecticut Sen. Joe Lieberman (I) indicated Sunday that he is unlikely to weigh in publicly on the Senate contest between state Attorney General Richard Blumenthal (D) and Linda McMahon (R). 

In an interview on CNN's "State of the Union," Lieberman said, "There's a high probability that I'm going to spend the rest of this year focusing on my Senate responsibilities." Lieberman said he is leaning toward voting "quietly and privately" rather than making a public endorsement.

He did leave the door open to a possible endorsement of McMahon, the former World Wrestling Entertainment CEO who won her party's endorsement at the state convention in May. Shortly after, McMahon's primary opponent, former Rep. Rob Simmons (R) suspended his Senate campaign. But in an interview last week, Simmons would not rule out jumping back into the contest at some point. 

McMahon is self-funding her campaign and has already spent some $16 million of her own money on the race. McMahon has endured a series of negative stories that have focused attention on her tenure as CEO of WWE.

The primary is August 10.