Republicans have more seats up for re-election this year — and more where the outcome is uncertain — than Democrats do. Right now, seven Republican-held seats are considered tossups by the nonpartisan Cook Political Report.

In order to get the majority, Democrats need four seats if Hillary Clinton wins. If she loses, they need five, because the vice president gets a Senate vote in the event of a tie.

Why These Seven Seats Are Vulnerable

Six of the seats are held by first-term senators who were swept into office as part of a 2010 Republican wave but are also in states that voted for President Obama two years later. The states have a history of voting across party lines.

The seventh is the contest in Indiana to fill the seat of retiring Senator Dan Coats, a Republican. It became a tossup when Evan Bayh, the state’s former Democratic senator, entered the race.

These seven seats would be competitive even if Mr. Trump were not the nominee, said Jennifer E. Duffy, who analyzes Senate races for The Cook Political Report. The real question, she said, is whether he has made them even more vulnerable. “Before the conventions, that didn't really appear to be the case, but since the conventions there has been a lot of volatility in polls.”

A primary concern is that opposition to Mr. Trump will depress Republican turnout in November. Other than Senator Mark S. Kirk of Illinois, who rescinded his endorsement, the candidates are trying to walk a fine line between saying they support their party’s nominee (generally without naming him) and distancing themselves from his controversial statements, in the hope that Republicans will turn out to vote even if they don’t support Mr. Trump.

Who’s Most — and Least — at Risk

Of the seven Republican tossups, Mr. Kirk, running in heavily Democratic Illinois, is the most likely to lose his seat (one that was formerly held by Barack Obama), while Rob Portman of Ohio has the best shot at being re-elected, according to polling and previous election results.

Kelly Ayotte of New Hampshire, in a tough race with the state’s Democratic governor, is one of a handful of Republican senators who have spoken out against Mr. Trump, though she says she still supports him.