Nearly six in 10 Americans want to unseat their own member of Congress, according to a new poll.

The George Washington University Battleground Poll shows just 26 percent of people say their own member of Congress deserves reelection, while 58 percent say it's time to give someone new a chance.

The poll is the latest to show a sharp rise in anti-incumbent sentiment following the government shutdown last month, but few have shown it in such stark relief. While Americans are generally happy to "throw the bums out" when it comes to the unpopular Congress, they are often much more supportive when it comes to their own member.

A Wall Street Journal/NBC News poll last month showed a similar portion -- 60 percent -- of Americans say they would unseat every member of Congress, including their own, if they could. But the new poll asks specifically about people's own member of Congress -- making that 58 percent figure all the more striking.

A Washington Post-ABC News poll around the time of the shutdown also showed a spike in anti-incumbent sentiment, with 24 percent saying their own member deserved reelection and 66 percent saying they want to "look around" for someone else to vote for.

By contrast, a Gallup poll conducted on the eve of the 2012 election showed 59 percent of Americans saying their own member deserved reelection.

According to Gallup's poll, it's rare that support for one's own member of Congress dips below 50 percent, much less 30 percent.

At the same time, this anti-incumbent mentality shouldn't be oversold. While the numbers could give members pause when it comes to their primary campaigns and if they are in competitive districts, strong primary challengers remain rare, and the vast majority of districts are very safe from flipping to the other party.

The new numbers notably show that this anti-incumbent sentiment is significantly stronger in Republican-held House districts and states where GOP senators face reelection in 2014.

While 50 percent of people in Democratic-held districts say it's time for someone new, 65 percent say the same in GOP-held districts. In states where Democratic senators face reelection in 2014, 53 percent say it's time for someone new, while 64 percent say the same in GOP states.

Where the partisan trend ceases is in states where governors face reelection in 2014. While 59 percent want to unseat their Democratic governor, just 52 percent want to unseat their Republican governor.