Obama is playing tougher, and thus far, playing tougher has worked for him.
Already, the president has forced two GOP retreats, first at the fiscal cliff, then over the debt ceiling. Plainly, he's intending to force more.
On climate, for example, he has a weapon in his back pocket: the Supreme Court's 2007 decision in Massachusetts v. EPA, which allows the EPA to regulate carbon dioxide as a pollutant. The president might wish Congress to enact a carbon tax or a cap-and-trade scheme, but he does not need Congress: he can proceed without.
On immigration, likewise, the president has a secret weapon: the GOP wants to make an immigration deal nearly as badly as he does. The GOP donor class quietly favors the president's immigration ideas as a source of cheaper and more tractable workers. The GOP's pundit class has convinced itself that low-income Hispanics will vote as "natural conservatives." And GOP practical politicians are terrified of doing anything described as offensive to Hispanic voters in the here and now, no matter how much that "anything" undermines their position in the future.
There do remain issues where the president will need Congress, of course. Yet on those issues too the president knows exactly where his best leverage is: the public image of Republicans in Congress as extremist, exclusive, and reckless. The president slammed his opponents as partisans of "the privileges of a few" who "mistake absolutism for principle … substitute spectacle for politics … [and] treat name-calling as debate." The danger of it is, that the largest part of the public agrees with him.
Plainly, the methods the GOP have been using have not been working. What should be done instead?