But they’re playing defense in several states, and have only a handful of opportunities to win a Republican-held seat among the 13 competitive Senate elections , according to race ratings provided by the Cook Political Report , a nonpartisan election handicapper.

Here’s the latest on the state of the race.

For a moment in September, it seemed Democrats had an opportunity to defy a deeply challenging map and regain control of the Senate. But the bruising fight over whether to confirm Justice Brett M. Kavanaugh appears to have jolted Republican voters who had been less enthusiastic than Democrats about the midterm elections. The Supreme Court clash seems to have nationalized many Senate races.

With Election Day around the corner, higher Republican intensity has created difficulties for Democrats because of where the battle for the Senate is taking place. Of the 13 most competitive races, 10 are in states President Trump carried.

Democratic senators like Heidi Heitkamp of North Dakota, Claire McCaskill of Missouri and Joe Donnelly of Indiana — who are all running in states Mr. Trump won by double digits — have come under attack for their opposition to Justice Kavanaugh. Each has been eager to change the subject, but they are widely seen by officials in both parties as the most vulnerable incumbent Democrats.

Also thought to be vulnerable is Senator Bill Nelson of Florida, a Democrat who is facing Gov. Rick Scott. Mr. Scott has poured millions of dollars of his own money into the race and enjoyed days of local media exposure in the aftermath of Hurricane Michael.

Democrats are hoping to capture four Republican-held seats. But in two of them — Texas and Tennessee — polls taken after the Kavanaugh confirmation showed their candidates slipping.