I agree with much of what new Conspirator Eric Posner says about Russia in his recent post. Under Putin, Russia has clearly turned against Western liberal values and reasserted an ugly form of traditional Russian nationalism. It is also clear that Putin has no sympathy for either the American project of spreading liberal democracy or the Western European effort to promote international human rights law.
At the same time, the new Russia is less of a threat to American global hegemony than many understandably fear in the aftermath of events in Georgia. Relative to its Soviet predecessor, Putin's Russia is weak in both hard military power and the ideological influence of "soft power." It will also be difficult for Russia to establish a working alliance with either China or the radical Islamists, the two other significant forces with an interest in undermining American dominance.
Let's take the hard power first. The Soviet Union was able to pose a serious military challenge to the US by pouring vast resources into its military - as much as 40 or 50 percent of GDP, according to some estimates. Today Russian military spending is a tiny fraction of America's (about 10%). Even if it wanted to, Putin's regime lacks the power to impose the kinds of draconian sacrifices on its people that it would need in order to rebuild its military power to Soviet-era levels. The poor performance of Russia's military in conflicts with weak adversaries such as Georgia and the Chechen rebels suggests that its forces have deteriorated in quality as well as quantity.
Russia's "soft power" deficit is even more glaring than its relative lack of military power. Unlike Communism, which at its height appealed to intellectuals and others all over the world, the ideology of Russian nationalism has little if any appeal to anyone who isn't Russian. Indeed, most of Russia's neighbors find it offensive and threatening, which is why they are now uniting behind Georgia and drawing closer to the West. States such as the Ukraine, Poland, and the three Baltic countries are no match for Russia individually; but they can certainly hope to counter it collectively - especially given the poor state of the Russian armed forces. The more nationalistic and aggressive Russia becomes, the more its neighbors - most of whom have powerful historical memories of brutal Russian imperialism - are likely to unite against it.
Russia will have great difficulty in cooperating with either China or the radical Islamists, the two other major forces in world politics that seek to challenge American dominance. China and Russia are competing for influence in the oil-rich states of central Asia, and the Russians are well aware that Chinese nationalists have longstanding territorial claims on Russia's far eastern possessions. This doesn't rule out occasional Russo-Chinese cooperation against the West, but it does make a close alliance unlikely. In the case of the Islamists, a Russian nationalist regime would be reluctant to engage in more than very limited cooperation because Russia itself has a large and potentially restive Muslim population (about 10% of its people). Strengthening radical Islamism increases the chance that Russia's own Muslims will start to resist Moscow's rule, and the Russians surely don't want to repeat their painful experience in Chechnya on a larger scale.
Finally, it is far from clear that Russia will continue on the course set by Putin. If oil prices decline and Putin's military adventures meet with setbacks, the political pendulum could swing back in favor of more liberal forces. Similar nationalist regimes have evolved into liberal democracies in many Latin American and East Asian states. The same thing could happen in Russia over the next decade or two. Although I don't have space to argue the point in detail, I don't think that Russian culture is any more intrinsically inimical to liberal values than those of Korea, Taiwan, or various Latin American states - all of which successfully transitioned from authoritarian nationalism to liberal democracy over the last 25 years.
The rise of authoritarian nationalism in Russia is a tragic setback for liberal values, and poses some difficulties for American foreign policy. But we should keep the magnitude of the threat in proper perspective. Putin's Russia is a serious menace to its neighbors, though even they can minimize the threat if they cooperate with each other and with the West. It is only a modest danger to us.