"Huge majorities" is a relative matter. The fundamental problem is that Obama, even with his mandate, came in trying to work with the Republicans. As such, when the rules of the Senate were on, they did not do what the Republicans under Bush II had done: essentially eliminate the power of the filibuster.

Unless you have the supermajority needed to overcome this, you are crippled when the opposition says "We don't care how much you wish to work with us, we don't want to work with you." The issue was not the effort to govern bipartisanally, the issue in this case was "are you willing to be the bad guy in public?"