Shane Goldmacher

The president’s popularity has ticked up slightly, though voters still view Donald J. Trump more favorably and have dour views of the economy.

The share of voters who strongly disapprove of President Biden’s handling of his job has reached 47 percent, higher than in Times/Siena polls at any point in his presidency.

Their approaches to immigration represent a test of voters’ appetite for the messiness of democracy, pitting the president’s belief in legislating against his rival’s pledge to be a “Day 1” dictator.

Ms. Haley campaigned more aggressively. She spent more on television advertisements. She raked in more money. She lost decisively.