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America's response is typically schizophrenic (link).
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On the one side, we have a politic class - steeped in the Cold War, that automatically assumes every positive for Russia is a negative for us.
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Then there are those who have their panties in a wad because Russia and Iran and working together to save their ally (Syria) from toppling. Russia plus Iran must equal evil.
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Then we have some people who think, so what. The US wants boots on the ground against ISIS, and if Russia does it good on this.
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I am definitely in the later camp. We have been in a defacto alliance with Iran and Iraq against ISIS for over a year. The US, Iran, Iraq and now Russia, all think it is critical to get rid of ISIS.
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Now, after the hoped for end of ISIS, our desired outcomes diverge. The US wants Syria's current leadership to step down (always a pie in the sky hope). We have trained non-ISIS anti-Bashar forces, only to see them melt away.
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Russia and Iran wand to prop up Bashar al-Assad after getting rid of ISIS.
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So, there will be a lot of talk of "losing" Syria in the future, but it was never ours (the US) to win or lose. And, if you are looking for a strategy against Russian power, there are few better than to have their military drawn into a middle-east civil war.
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What we should NOT do is make the mistake we made in Afghanistan. That is, after Russia has put down this rebellion, we should NOT supply ISIS with weapons to attack Syria's Bashar al-Assad. We should, to quote Snagglepuss, "Exit - Stage Left."