Instead, he asked congressional Republicans who have resisted new taxes at every turn over the last six years to raise taxes on the wealthy. He asked lawmakers who won their seats on promises of reining in government to reopen the spending spigot to provide free community college, child care and paid parental leave to millions of middle-income Americans. The program he outlined sounded pretty much like the one he would have sent to a Democratic Congress.

“If you share the broad vision I outlined tonight, join me in the work at hand,” he told lawmakers. “If you disagree with parts of it, I hope you’ll at least work with me where you do agree. And I commit to every Republican here tonight that I will not only seek out your ideas, I will seek to work with you to make this country stronger.”

But after the lights went out and the presidential motorcade had made its way back up Pennsylvania Avenue, the party balance had not changed. For all of Mr. Obama’s confident demeanor, the question raised by the speech was whether advancing initiatives with little or no hope of passage constituted an act of bold leadership or a feckless waste of time.

Every president throws out ideas in a State of the Union address knowing they will not succeed, at least not right away — to frame the debate, lay down an opening bid, draw a line against opponents or set the stage for future action. But rarely has the disconnect between a president and Congress seemed as wide as it is now.