Putin has a big problem in Syria — one to which Western coverage of the Russian military intervention in Syria has not paid much attention.

Namely, the intervention is not at all popular with Russians themselves. Because Putin's personal popularity is key to his political longevity, that could be a very serious matter indeed for the Russian leader.

A recent poll by Moscow's Levada Center shows that only a small minority of Russians support giving Bashar al-Assad direct military support. Only 39 percent of respondents said they supported Russia's policy toward the Assad regime. When asked what Russia should do for Assad, 69 percent opposed direct military intervention. A tiny 14 percent of respondents said that Russia should send troops or other direct military support to Syria.

It's clear that Putin is taking those concerns seriously. In what seems to be an attempt to shore up public opinion among Russians who are worried about casualties in a faraway war, the Kremlin has already promised that only volunteers, not conscripts, will be sent to Syria, and that the military intervention will consist only of airstrikes.

But Putin's public opinion problems on Syria could be just the beginning. Russia's economy is already struggling, and a new war will be an expensive additional burden. If Russia's presence in Syria makes its forces a target of terrorist attacks there, or, worse, if it coincides with attacks at home, that could damage public opinion even further.

Russians' skepticism of Putin's Syria policy is especially stark when contrasted with the overwhelmingly positive response to his actions in Ukraine. That was a huge boost to Putin's popularity, helping his regime weather Russia's 2014 economic problems with high public support. But the Ukraine intervention led to sanctions on Russia, which proved unpopular with the Russian elites.

That's a problem for Putin, because he needs to keep elites happy in order to maintain their vital political support for his regime. If, as some commentators have suggested, the Syria intervention is an attempt to gain leverage to force the West to lift sanctions, then Putin may find that it simply exchanges one problem for another: Instead of public popularity and elite frustration, he would have happier elites but a less supportive public.

And that's assuming it works, which it might not. For one thing, it's not clear that Putin will be able use Syria to gain leverage at all, which could mean that he is left with a less enthusiastic public and still has no sanctions relief to offer elites.

Even if Putin does manage to pull it all off, using his unpopular intervention in Syria as a bargaining chip to reduce Western sanctions on Russia, the trade-off might not be worth it.

As Russian analyst Alexander Verkhovsky explained to me when I met with him in Moscow last spring, Putin's popularity is his "principal resource." As long as Putin is popular, his position is fairly secure. But if his popularity ratings falter, then he risks being pushed out of office by Russian elites in favor of someone else who can better protect their interests — as Verkhovsky put it, he can be "changed for another guy, even someone from the same [Putinist] circle." So even if Putin is able leverage the intervention in Syria to offer elites the sanctions relief they want, that may come at too high a political price.

To be clear, none of this means that Syria will be enough to overcome Putin's reportedly sky-high approval, nor does it mean that one unpopular Mideast adventure is going to bring the downfall of the Putin government. But Putin's hold on power, as solid as it might look from the outside, isn't; it's beset by a number of problems and, at the moment, is premised in large part on overwhelming public support. With elites alienated, a hit to his poll numbers is also a hit to his basic legitimacy. That's a precarious position to be in, particularly given Russia's current economic downturn. No single unpopular policy is going to bring it all crashing down, but the point is that he's not in a position to go gambling with his popularity, and yet he's just done exactly that.

In other words, while it may look like Putin is pursuing a grand, brilliant gamble in Syria, the reality is that he may have just made the worst kind of bet: one in which he'll be the big loser at home, no matter the outcome in Syria.