It has been a brutal month for President Obama. The historic electoral rebuke delivered to his party was followed at the G-20 meeting by a public rebuff of the Federal Reserve's QE2 program and the administration's handling of the China currency issue.

The president arrived home to find House Democrats intent on keeping Nancy Pelosi as leader, New York Congressman Charles Rangel judged guilty by a House ethics panel of 11 violations, and a lame duck session of Congress fraught with battles over taxes, the New Start treaty and more. This has Republicans feeling cocky about 2012.

Opinion surveys give some support for GOP optimism. This month's Associated Press-GfK poll shows only 39% of Americans believe Mr. Obama deserves re-election, while 54% believe he deserves to be voted out of office. In a late October CNN poll, Mr. Obama trailed both Mitt Romney and Mike Huckabee nationally. And in polls taken in battleground states by Public Policy Polling, Mr. Obama lost to a generic unnamed Republican in Pennsylvania, New Hampshire and Colorado.

Mr. Obama can't count on a strong economy to improve his fortunes. President Ronald Reagan's policies produced 4.5% and 7.2% growth in the two years before his 1984 re-election. But the University of Michigan Economic Forecast projects only 2.3% and 3.2% growth in 2011 and 2012, respectively, and 9% unemployment at the next election.

Still, Republicans should sober up. It is always difficult to defeat a sitting president. Since World War II, three have been defeated for re-election and two decided not to run again. But five have sought and won second terms.

Karl Rove is a former senior adviser to President George W. Bush. He is a Fox News contributor. To continue reading his column in The Wall Street Journal, click here.

Karl Rove joined Fox News Channel as a political contributor in February 2008. He also currently serves as a columnist for the Wall Street Journal. Mr. Rove helped organize the political-action committee American Crossroads. His latest book is "The Triumph of William McKinley: Why the Election of 1896 Still Matters" (Simon & Schuster, 2015). Follow him on Twitter @KarlRove.