Sen. Joseph Liebermana at the Capitol Hill in Washington on June 17, 2008. (UPI Photo/Patrick D. McDermott)

HAMDEN, Conn., July 2 (UPI) -- Sen. John McCain would do little to cut Sen. Barack Obama's commanding lead in Connecticut by adding Sen. Joseph Lieberman to his ticket, a poll indicated.

The Quinnipiac University Polling Institute found that Obama, the presumptive Democratic nominee from Illinois, leads among likely voters and among nearly all sub-groups in the state.

"At this stage of the campaign, Sen. Barack Obama is rolling over Sen. John McCain in Connecticut," Poll Director Douglas Schwartz said. "Quinnipiac University also has conducted surveys in seven swing states in the last two weeks and Sen. Obama is ahead in every one."

Lieberman, Al Gore's vice presidential candidate in 2000, ran for the Senate as an independent in 2006 after losing the Democratic primary. He has continued to caucus with the Democrats in the U.S. Senate but agrees with McCain, the presumptive Republican nominee, on Iraq and has endorsed him.

The poll also found that a majority of Democrats would like Obama to pick Sen. Hillary Clinton, D-N.Y., as his running mate. But both independents and Republicans oppose the move.

Overall, Obama has a 56 percent to 35 percent lead over McCain among likely voters in the state. Only 14 percent said they would be more likely to vote for the Arizona senator with Lieberman as vice president on the GOP ticket, while 32 percent said they would be less likely.