Like a guerilla army, never go to a shutdown (a general engagement), but keep coming up with cuts, compromising, letting the government stay open for a few more weeks, letting the debt limit rise a few hundred billion, and then come back for more cuts and repeat the cycle.
And don't just demand spending cuts. Go for defunding of Obamacare, blocking the EPA from carbon taxation and regulation, a ban on card check unionization, and constraints on the FCC's regulation of the Internet and talk radio. Put those items on the table each time, each session.
Every time the issues come up, every time the cuts are litigated, Obama's efforts to appear to be a centrist will be frustrated. Time and again, he will have to oppose spending cuts. Over and over, he will come across as the liberal he is, battling for each dime and opposing any defunding.
Obama's campaign strategy has two elements: Change the subject from the 09-10 agenda, and move to the center. A tough, determined Republican budget offensive, embracing all these elements and fought in this guerilla style, will frustrate both and lead to his defeat.