Fifty-five percent of registered voters approve of the way Gov. Bob McDonnell (R) is handling his job, while 26 percent disapprove, according to a poll released Wednesday by Quinnipiac University.

The Connecticut university’s first poll on Virginia political issues also indicates that many more voters personally like McDonnell than approve of his policies. Voters like McDonnell personally by a margin of 57 percent to 16 percent. But when asked if they like most of his policies, support drops to 48 percent to 33 percent.

Among independent voters, 59 percent approve of McDonnell’s job performance, while 24 percent disapprove.

“Gov. Bob McDonnell’s overall support levels are among the highest when compared to other governors around the country,” said Peter A. Brown, assistant director of the Quinnipiac University Polling Institute. “And they are far better than those of his GOP counterparts in Florida, Ohio, New Jersey and Pennsylvania.”

The independent Quinnipiac poll, conducted by live interviewers with registered voters on land lines and cell phones, releases periodic voter surveys of office holders, candidates and issues nationally and in Connecticut, New York, New York City, New Jersey, Pennsylvania, Ohio and Florida. On Wednesday, it added Virginia, increasingly considered a swing election state, to its mix.

Virginia Lt. Gov. Bill Bolling (R), who is running for governor in 2013, has a 39 percent approval rating, with 20 percent of voters disapproving and 42 percent undecided.

State Attorney General Ken Cuccinelli, who had made a name for himself suing the federal government, has a 49 percent approval rating, with 31 percent of voters disapproving and 20 percent undecided.

The divided Virginia General Assembly received a 48 percent approval rating, with 33 percent disapproving.

Voters oppose, 52 percent to 41 percent, a law that would allow same-sex couples to marry. But they support, 51 percent to 43 percent, allowing same-sex couples to adopt children.

Voters say state-run agencies should not ban prospective parents from adoption based on sexual orientation by a margin of 59 percent to 35 percent. But voters say church-run agencies can continue to ban the practice by a narrow 48 percent to 45 percent.

On another timely issue, voters split down the middle, 41 percent to 41 percent, on whether to continue to ban uranium mining in the state. Virginia Uranium is lobbying legislators to lift the ban so it can mine what is believed to be the largest deposit of uranium in the United States, in south central Virginia.

Quinnipiac University surveyed 1,434 registered voters June 21 – 27. There is a margin of error of plus or minus 2.6 percentage points.