The co-chairman of the Congresional Russia Caucus said today that he’d have serious second thoughts about letting his family go to Sochi for the Winter Olympics given the security risks.

Asked by CNN if Americans should go to the Games, Rep. Michael Grimm (R-N.Y.) responded that his “natural instinct would be to say yes, because you don’t want the terrorists ultimately to win.”

“You know that’s what — you know, the — one of the main goals of terrorism is to invoke fear and stop people from living their daily lives. And we don’t ever want to completely give into that,” Grimm said.

“But I would be disingenuous not to say that I have serious concerns. And if you are asking me, would I send my family there, I would have trepidation because there are serious and credible threats that we know about and I’m not completely convince that the Russians will be able to completely keep us safe,” he added. “And that being said, it’s not a slight against Russia. No one can completely keep you safe, not against terrorism. There’s just too many vulnerabilities.”

Wanted posters have been posted at hotels around Sochi looking for Ruzanna “Salima” Ibragimova, the widow of a terrorist from the Caucasus, fearing that she may have already arrived in the region and is planning “a terrorist act within the 2014 Olympic region.”

The Volgograd bombers also left behind a video that was posted on a jihadist web forum Sunday, promising, “We’ve prepared a present for you and all tourists who’ll come over. If you will hold the Olympics, you’ll get a present from us for the Muslim blood that’s been spilled.

The Pentagon said Monday evening that it’s prepared to offer air support and two ships in the Black Sea to Russia to protect the Sochi Games.

“I think they’re doing the very best they can,” Grimm said of Russia’s security efforts. “…When you talk about security, it’s basically like an onion. And the very center of the onion is the area most protected. So if you’re going to be in the venue watching the actual competitive games, that’s probably the safest place to be because that’s where the concentration of security will be.”

“But as you go out and you start to peel away the layers of that onion, the outer most layers are your most vulnerable areas. So for people that are going, obviously they want to see the games. But they also want to see Russia. They want to enjoy the culture. They want to do what most tourists do. And I don’t believe you’re going to be able to make sure that every restaurant, every museum, all the tourists spots that could be a mile, two miles away from the actual competitive games and from these stadiums, there’s absolutely no way you can keep all of those safe.”