Hillary Clinton may be surging in national polls, but in the key swing states of Florida, Ohio and Pennsylvania, Donald J. Trump remains in striking distance.

According to a group of surveys of likely voters released on Tuesday by Quinnipiac University, Mrs. Clinton holds a one percentage point lead in Florida, a four-point lead in Ohio and a 10-point lead in Pennsylvania over Mr. Trump. The polls, which had a margin of error of plus-or-minus three percentage points, are slightly closer when Gary Johnson and Jill Stein, the Libertarian and Green Party nominees, are included.

Since 1960, no presidential candidate has won the White House without winning two of the three states. The poll results offer Mr. Trump, the Republican nominee, a ray of hope after more than a week of turmoil in his campaign.

Although Mrs. Clinton still holds an advantage in the states, it is not her popularity with voters that is keeping her afloat. It is even deeper concern about Mr. Trump, the polls suggest.