Democrats, Ms. Pelosi told Mr. Biden and a group of his aides, need a more succinct and consistent message. The speaker, who has long been fond of pithy, made-for-bumper-sticker mantras, offered a suggestion she had heard from members: Democrats deliver.

What Ms. Pelosi did not fully detail that February evening was that some of her party’s most politically imperiled lawmakers were revolting against Mr. Biden’s preferred slogan, “Build back better,” believing it had come to be a toxic phrase that only reminded voters of the party’s failure to pass its sweeping social policy bill. And what the president and his advisers did not tell the speaker was that they had already surveyed “Democrats deliver” with voters — and the response to it was at the bottom of those for the potential slogans they tested, according to people familiar with the research.

No new campaign message was agreed to that day — or since. Mr. Biden is now absorbed by the war in Europe. Facing the biggest foreign policy crisis of his presidency, he is hardly consumed with the looming midterm elections, let alone trying to devise a catchy slogan. Still, his advisers acknowledge that the crisis in Ukraine presents a chance for a reset, perhaps the president’s best opportunity to restore his standing before November.