“At this stage of the campaign, Republican U.S. Senate candidates may be running against their own presidential nominee, Donald Trump, as much as they are against their Democratic opponents,” said the poll’s assistant director, Peter Brown. “But if Trump continues to lag behind in the presidential race, that will make it more difficult for GOP candidates, logic holds, up and down the ballot.”

These Republican incumbents, therefore, find themselves in a difficult position when it comes to supporting Trump. Illinois Sen. Mark Kirk, who is in a tough race that has analysts predicting his defeat, has denounced his party’s nominee, seeing no political benefit to doing otherwise. For others, though, the strategy is not cut and dried. While few are inclined to appear with the nominee or mention his name on the stump, opting instead to localize their own races, there are also perils to cutting ties altogether.

“You can’t rule that out it discourages Republicans and hurts their turnout,” says Terry Madonna, director of the Franklin and Marshall poll in Pennsylvania.

One veteran Republican operative who was involved in the 1996 effort cited exactly that reason in saying the RNC is unlikely to withhold support for the nominee: “If you pull the plug on Trump, you’re going to be writing off a significant percentage of Republican voters.”