Voters in 10 competitive House battleground districts remain deeply divided on Brett Kavanaugh’s nomination to the Supreme Court, according to a wave of New York Times Upshot/Siena College polls.

But there are signs his support is eroding.

Over all, 44 percent of likely voters in the districts said they supported Mr. Kavanaugh’s nomination, with 45 percent opposed. Among all registered voters, 40 percent supported Mr. Kavanaugh, and 43 percent were opposed.

The surveys were conducted after the initial allegation that Mr. Kavanaugh sexually assaulted a woman when they were both teenagers, and before other allegations of sexual impropriety surfaced.