President Obama's 2012 budget is not a serious governing document. It's a political one, designed to boost his re-election chances.

By repeatedly saying that his budget reduces the deficit by $1 trillion over 10 years, he hopes the numbers make him sound fiscally conservative. But he puts off 95% of the deficit reduction until after his term ends in 2013. And he assumes that economic growth in the next few years will be at least 25% higher than credible economic forecasters estimate.

Mr. Obama's budget includes $1.6 trillion in tax increases that are real enough—but most of the spending cuts are not. For example, as Rep. Paul Ryan, the House Budget Committee chairman pointed out to me, the administration projects war costs for Iraq and Afghanistan at surge levels for the next decade, and then conjures up about $1.3 trillion in defense savings by assuming drawdowns in each theater -- drawdowns that were already in the cards. Outside of this sham transaction, according to Mr. Ryan, there are only $104 billion in real spending cuts over the next 10 years.

Mr. Obama wants House Republicans to take the lead in cutting current spending and proposing future restraint in entitlement and other mandatory spending. He's betting that letting Republicans take the lead will cripple them. This misreads public opinion. But it is plausible to believe that Republican mistakes can help revive Mr. Obama's political fortunes. So it's important that the GOP offers real budget cuts without coming across as angry and frenetic. Republicans need to patiently show what they are doing and why, and to express their sadness and disappointment over Mr. Obama's failure of leadership.

Mr. Rove, the former senior adviser and deputy chief of staff to President George W. Bush, is the author of "Courage and Consequence" (Threshold Editions, 2010)

Read Karl Rove's Complete Column on the GOP and the Budget at WSJ.com

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.