Privately, though, many Republicans were seething.
It was a long way from the Barack Obama of 2009, the brash young idealist who promised to change the way Washington worked, seek post-partisan solutions and banish "the stale political arguments that have consumed us for so long."
This year, instead of an outstretched hand, he delivered a slap. "We cannot mistake absolutism for principle, or substitute spectacle for politics, or treat name-calling as reasoned debate," he said.
Obama has been trying this more pugnacious approach since the November election, and it has undeniably made him more effective — so far. He forced Republicans to back down on income tax rates at the edge of the "fiscal cliff," and he appears to have forced them to back down again on their threats to block an increase in the federal debt ceiling.
It's impossible to blame any politician, even a president who once promised post-partisan hope and change, for surrendering to reality and doing what works. But it sure isn't pretty, and, more important, it may not always be effective.
At some point, Obama is likely to need willing collaborators from the opposition — if he hopes to pass an immigration reform law, for example, or negotiate a long-term deal to reduce the deficit.
When that day comes, the president may find himself wishing he had devoted a few more words of his second inaugural address to offering an outstretched hand.