Here’s a Rasmussen poll suggesting that the public at large doesn't have that much patience:
Granted, the budget deficit and Republican's zeal to defund ObamaCare might still be sucking all the political air out of Washington between now and November, 2012. And unless there’s something in the water supply that makes them nominate Ron Paul, the Republicans aren’t going to be making an issue of ending the Afghanistan war in 2012. But they might start complaining about Obama's flawed military strategy, especially if General Petraeus is no longer around to lend it his prestige. And an anti-war rebellion in Obama’s base certainly isn’t out of the question, especially if people like Nancy Pelosi and Sherrod Brown start complaining publicly about a quagmire.“A majority of voters, for the first time, support an immediate withdrawal of all U.S. troops from Afghanistan or the creation of a timetable to bring them all home within a year. A new Rasmussen Reports national telephone survey finds that 31% of Likely U.S. Voters now say all troops should be brought home from Afghanistan immediately, while another 21% say a firm timetable should be established to bring all troops home within a year’s time. The combined total of 52% who want the troops home within a year is a nine-point jump from 43% last September. Just 37% felt that way in September 2009.”
It wouldn't take a serious anti-war primary challenge to leave Obama in a political position a little like Lyndon Johnson’s in 1968. That’s not a great place for a sitting Democratic president to be.