"If we do not support our team and show up, I think the terrorists are winning. And that's what they're trying to do. Having said that, I would say the security threat to the Olympics, this particular Olympics, are the greatest I think I've ever seen because of the proximity of the terrorists to the Olympic village," he said on CBS' "Face the Nation."
The comments come as three terrorist attacks in Volvograd, 600 miles from Sochi, by suspected Islamist militants from the Northern Caucasus region since October has raised the specter of threats to the more than 10,000 Americans expected to attend the Olympics.
McCaul said he wouldn't rule out pulling Americans out of the games, but that it's too soon to "be an alarmist." McCaul noted that Russian President Vladimir Putin is "is putting everything he has from a security standpoint down there," though he said the threat of attacks outside the village still persisted.
Appearing on CNN's "State of the Union," Russian Ambassador to the United States Sergey Kislyak said he was confident the games would be safe.
"It's not only that I believe. I'm absolutely certain," he said.