Really, Putin's only popular since we don't have any reasonable alternative which would be 1) not oligarchs 2) not batshit-crazy.
And I think therein lies the problem most foreigners see: there is no viable, antagonistic opposition. While I certainly wouldn't say the US government is a shining beacon of efficiency, the highly antagonistic party politics ensure that if any major change takes place, either everyone agrees on it or it will grind on for so long that everyone saw it coming and had been discussing it for years.
From that starting point, it all comes down to a thought experiment: What would happen if some person in the government was replaced with a body-double with the brain of Hitler?
For Obama-Hitler, he would end up politically hamstrung; and wouldn't be much more or much less able to get his agenda through the legislature than he is now. Likewise, the army would be pretty much off limits. However, he would be able to use executive agencies like the CIA, NSA, and such to carry out his agenda. Their power is limited by oversight; but it is oversight which is historically ineffectual and blind to most goings-on. Alternatively, if the head of one of those agencies with little oversight was replaced with a *-Hitler, they could potentially orchestrate enough sneaky stuff to at least have some considerable manipulative power in the political system. This is the main reason Americans fear the expanding powers of groups like the NSA: a lack of an antagonistic system of governance.
If it were Putin-Hitler, or whomever-is-designated-his-replacement-after-Putin-eventually-retires-Hitler, he would currently have a much easier time of it than Obama-Hitler. Without reasonable, antagonistic alternatives, Russia is setting itself up for a fall, or worse. That is largely why the internal situation of Russia makes those outside nervous, especially when approval ratings are so high that a unified opposition couldn't arise.