With House Speaker John A. Boehner’s decision to back away from a “grand bargain” on the budget, President Obama may be forced to recalibrate his goals and his strategy to show that he can bring the negotiations to a successful conclusion.

Throughout the spring and the summer, he has tried to set himself apart from Republicans and many Democrats as the leader most determined to solve a big problem with a big solution and as the politician most willing to make real compromises to get there.