There is a second critical contest in America’s 2016 elections: the battle for control of the Senate.

Republicans, pessimistic about their presidential prospects, feel an urgency to hold on to the Senate, where they now effectively have a 54-to-46 advantage. (Democrats would have to score a net gain of 30 seats to win a majority in the House, a highly unlikely prospect.) Both parties acknowledge that the Senate is a tossup that will be affected by the presidential election. But there are two other, perhaps more important, factors: the outcome of a number of remaining primaries and the question of whether congressional Republicans, especially the speaker of the House, Paul D. Ryan, can fashion an agenda that, if necessary, creates a distance from the debates of the presidential race.

Strategists on both sides suggest that there are two Republican-held seats that lean Democratic, along with several tossups. There is only one Democratic-held seat, that of the party’s Senate leader, Harry Reid of Nevada, who is retiring, that seems competitive. But there are three or four other Republican-held seats that may be vulnerable if the presidential race proves a landslide for the Democrats.

Democrats, however, say that a couple of primaries will be critical: In Pennsylvania, party leaders believe that if Katie McGinty, an environmentalist, can emerge the winner in her close contest next week, she has a chance to unseat Senator Patrick J. Toomey, the incumbent Republican, in November. Later, if Representative Patrick Murphy, a Florida Democrat, is able to defeat a challenger from the left who faces ethics charges, he will be the favorite to take the seat vacated by Senator Marco Rubio, a Republican.