PHOENIX — The Southwest has emerged as a key battleground for control of the United States Senate in the final days of the turbulent midterm election, with off-the-charts early voting numbers giving Democrats hope that they can win tight races in Arizona, Nevada and maybe, just maybe, the bank shot of them all, Texas.

Republicans have been dominant for years in Arizona, which has not elected a Democratic senator since 1988, and senators have a good track record at winning re-election in Nevada, where Dean Heller, a Republican, is now seeking a second term. But Nevada polls recently have shown Mr. Heller and the Democratic nominee, Representative Jacky Rosen, trading off in the lead; Arizona polls have shown a neck-and-neck race between the Democrat, Representative Kyrsten Sinema, and the Republican, Representative Martha McSally.

The mere fact that the Republican Senate candidates haven’t put away the race in those two states has been enough to lead some Democrats to think that Tuesday's election could lead to a very late night, with the East Coast waiting for the results out West to see who controls the Senate. Republicans now have a single-seat majority.

[Take a look at the Senate races to watch]

As for Texas, there are signs that Beto O’Rourke, the Democratic nominee, has tightened his race against Senator Ted Cruz, the incumbent Republican. Still, Mr. Cruz holds a lead in recent polls, and no Democrat has won statewide in Texas since 1994.