Russian President Vladimir Putin listens to Chechen leader Ramzan Kadyrov (not pictured) during their meeting in Novo-Ogaryovo residence outside Moscow on August 7, 2013. - 

How closely are U.S. businesses watching the Obama/Putin spat? It depends who you are. If you’re a huge multinational, you’re really not worried about the bilateral bickering.  That's according to Anders Aslund, a senior fellow at the Peterson Institute for International Economics.

“Coca Cola, McDonald's, Proctor and Gamble are very big and very happy in Russia," Aslund says.

Boeing exports planes to Russia. GM sends cars. But other U.S. companies aren’t so big and happy. They’re still trying to get into the Russian market -- which, by the way, loves Western products, and they can afford them.

“Moscow is just booming, and the money is everywhere to be seen," says Steve Sestanovich, who  handled Russia policy in the Clinton administration.

U.S. companies still trying to latch onto the boom could feel the chilly breeze between the White House and Kremlin. It’s not easy doing business in Russia. You have to slog through miles of red tape, and Russian bureaucrats could see Putin’s behavior as a signal to throw up roadblocks to American investors.

“If you’re an investor, and you’re trying to build a factory inside of Russia, you’re going to have to start begging for favors from people in the Russian government," says Moyara Ruehsen, who teaches international economics at the Monterey Institute. "So, yeah, that’s going to get tricky.”

Ruehsen says Russia isn’t a huge market for the U.S. especially compared to China and Brazil. For now, at least, that’s not likely to change.