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But lying low cannot be easy for a president who promised immigration reform to the nation's Latino and Asian voters, who overwhelmingly backed Obama's reelection in November. Indeed, five undocumented immigrants were in the audience Tuesday night.

“It’s a Catch-22 for him,” Rep. Raul Labrador of Idaho, a leading Republican advocate in the House for immigration reform, said Tuesday night just outside the House chamber. “If he talks too much about it, then it looks like he’s pushing his agenda down our throat. And if he doesn’t talk enough, then he gets criticized for that.”

Many Republicans said Obama had handled the immigration issue deftly.

“I thought on comprehensive immigration reform, I thought his words were measured," Rep. Paul Ryan (R) of Wisconsin, House Budget Committee chairman and a longtime supporter of immigration issues, told CNN. "I think the tone and the words he took were productive on that front.”