Russia siding with al-Qaeda in the midst of the Chechen Wars? Seems unlikely, especially with Zhirinovsky at the helm.
Now, Zhirinovsky did heavily back Saddam's Iraq, which might cause some problems.
"Worst case scenario" would probably be WMD usage, severe curtailing of civil liberties in the United States, widespread retaliatory anti-Islamic pogroms/riots, and a harsher military response from the U.S. (if WMDs are used against American civilians, the US might nuclear weapons might be utilized in response). The U.S. gets bogged down in an even worse quagmire as a wider-scale intervention is launched.
Meanwhile, a more aggressive Russia uses the harsh actions of the U.S. as an excuse to go all-out against Chechnya, utilizing chemical weapons and mass killings to crush resistance. They use either the Pankisi Gorge or Kodori crises (or something similar) as an excuse to invade Georgia. Meanwhile, China goes crazy on the Uyghurs.
The 2001 Indo-Pak crisis goes bad and both states nuke one another to pieces. Terrorists might obtain nuclear weapons in the aftermath. Famine and darkness falls across the world.
Russia backs it's allies in the Middle East, threatening "severe retaliation" if the U.S. intervenes against Syria, Iraq, Iran, etc. While Russia is none too popular in the Middle East, those regimes gladly accept Russian protection against an enraged America. Even though Russia is nowhere near it's Soviet-era might, the US decides that it does not want the headaches Russia could cause them and backs down. Even still, US-RU relations are at their lowest point since the Cold War.
In an effort to offset a more hostile America in the wake of the Georgian War, Russia decides to abandon its old commitments to stopping nuclear proliferation and aids the nuclear programs of those nations. Pakistani scientists out of a job after the destruction of their nation also make their services available. Despite the best actions of the U.S. and Israel, one of those states eventually obtains nuclear weapons, prompting a wave of nuclear proliferation across the Mideast.
Later on down the road, some crisis (Arab Spring gone bad, a second Iran - Iraq War, a Saudi-Iranian War, an Egypt-Libya War, another Arab-Israeli War, some civil war, foreign intervention, any combination of the above, etc) sets off the whole pile.
Unlikely, but I'm writing on the fly. A better writer could probably make things a lot worse and keep it plausible.