A new survey in Virginia found President Obama’s popularity eroding in the state, but his slide has so far not trickled downballot to hurt the Senate campaign of fellow Democrat Timothy M. Kaine.

The Quinnipiac University Poll shows 54 percent of registered voters in the state disapprove of how Obama is handling his job, up 6 points since late June, while 40 percent approve. In a state that Obama won convincingly in 2008, 51 percent now say that the president does not deserve four more years in office.

Obama runs a very close race in Virginia with the two leading Republican contenders for 2012. Obama gets 44 percent to Texas Gov. Rick Perry’s 42 percent, the poll shows, while he matches up with ex-Massachusetts governor Mitt Romney by a similar two-point margin tilting toward Romney.

In the Republican primary contest, Perry leads Romney, 25 percent to 19 percent. All of the other GOP contenders are in single digits, with Rep. Michelle Bachmann (Minn.) scoring 5 percent.

The likely race to succeed retiring Sen. James Webb (D) remains essentially tied between Kaine and George Allen (R), both former governors. Allen scores 45 percent in the Quinnipiac poll, and Kaine gets 44 percent.

The last Quinnipiac poll of Virginia, released at the end of June, showed Kaine with a tiny lead over Allen, 43 percent to 42 percent, and gave Obama identical approval and disapproval ratings of 48 percent.

Obama was the first Democratic presidential candidate in four decades to win Virginia, and Republicans have targeted the state as one of a handful that could swing away from the incumbent in 2012. Since Obama’s win in 2008, Republicans have picked up the governor’s mansion and three congressional seats. They could cement control of the General Assembly by taking the state Senate this November.

Obama does not have to win Virginia next year to secure reelection, but losing the commonwealth would make his path more difficult, analysts say.

National surveys have shown a clear erosion of support for Obama in recent months. Persistently high unemployment rates and increased fears that the economy is not recovering have contributed to his reduced standing, and many polls have shown his numbers slipping in hypothetical matchups against Republican challengers.

Quinnipiac notes that in Virginia, Obama’s job approval rating “is plummeting among independent voters,” with his disapproval going up 8 points in roughly six 10 weeks. While 67 percent of white voters in the state disapprove of his performance, 83 percent of black voters approve.

On the GOP side, Perry has strong leads over Romney among men and among white evangelical Christians, while women prefer Romney.

“Rick Perry’s campaign sees carrying the South in the nomination race as critical,” said Peter A. Brown, assistant director of the Quinnipiac University Polling Institute. “The data from the capital of the Confederacy gives him reason to be optimistic.”

But in hypothetical general election matchups with Obama, Romney does much better among independents than Perry does. Romney leads Obama by 9 points with independents, while Perry is tied.

In a Washington Post Poll of Virginia registered voters released in early May, 52 percent of respondents approved of Obama’s job performance and 43 percent disapproved. Obama led Romney in a hypothetical matchup, 51 percent to 41 percent. Perry was not included in the survey.

The Post poll showed Kaine and Allen tied at 46 percent apiece among registered voters. Quinnipiac still shows the Senate contest deadlocked — Allen has the overwhelming support of Republicans, Kaine the same with Democrats, and they are essentially ties among independents.

Men and older voters prefer Allen, while women, younger voters and those with college degrees give Kaine the advantage.

The question for Kaine is whether his electoral fortunes next year will track closely with Obama’s. As a close friend and political ally of the president — Obama hand-picked Kaine to serve as Democratic National Committee chairman — Kaine will always be linked to Obama and his policies.

But Kaine also has his own longstanding identity in Virginia, formed as Richmond mayor, lieutenant governor and then governor. He may retain the support of some Democrats who don’t back Obama.

On Wednesday, Quinnipiac released a separate portion of the same Virginia poll, showing both Gov. Robert McDonnell (R) and Sen. Mark Warner (D) with approval ratings over 60 percent.

The Quinnipiac survey polled 1,368 registered Virginia voters from Sept. 7-12. The margin of error is plus or minus 2.7 percent.