Just 37 percent of Americans approve of the job he is doing, according to the latest survey by the Pew Research Center, lower than any modern president after a year in office and no better for all of his efforts. Forty-one percent think he will be an unsuccessful president, twice as many as last year and nearly twice as many as those who think he will be successful. Far fewer Americans think he keeps his promises than thought so when he was inaugurated.

Mr. Trump’s outsize personality has so polarized the country that he may not be able to win over many converts easily, even with opportunities like a national television audience of tens of millions. His goal for the speech was to reach beyond his base and put forward a more optimistic, bipartisan face to a presidency that has been exceedingly divisive, but he has demonstrated before that such moments rarely last before he begins lobbing political artillery shells all over again.

“Every major address like this is an opportunity for reset, but that is unlikely in this case and even more unlikely still given that it’s an election year,” said Lanhee J. Chen, a scholar at the Hoover Institution at Stanford who advised Mitt Romney’s presidential campaign in 2012. “The current narrative, both for those who oppose the president and those who support him, has been established over the better part of two years — during a campaign and one year in office. It’s hard to see that changing dramatically.”

Matt Latimer, a former speechwriter for President George W. Bush, said the effect of a State of the Union address could be overstated, especially if it was not followed up consistently, and Mr. Trump has shown little capacity for that. “If past history is any guide, the president will only bask in praise for so long before he demonstrates his self-destructive tendency to undo it all in the form of an avoidable controversy or an offensive tweet,” he said.