Kremlin propagandists have not criticized Vladimir Putin directly but have taken aim at the chaos of his call-up of soldiers for his invasion of Ukraine.
Huge numbers of Russians are trying to flee Russia amid reports that mobilized troops face "mass incarceration."
"I expect he will be on the battlefield in Ukraine fighting for Putin any day now," Graham tweeted.
"They are likely to suffer a high attrition rate," the U.K.'s Defense Ministry said of the drafted Russian troops.
Edward Snowden has lived in Russia for nearly a decade, and on Monday was declared a citizen.
Last week, Russian President Vladimir Putin announced a partial mobilization of troops amid the ongoing war with Ukraine, which has increased tensions.
Russia faced criticism last week at the United Nations General Assembly for its aggression in Ukraine.
One 63-year-old man who has diabetes and a severe brain injury was among those called to fight after doctors told him he was fit for service.
In the days since a mobilization decree, huge lines of people have formed at Russia's borders with neighboring countries such as Georgia and Finland.
White House National Security Adviser Jake Sullivan warned Russia would face ""catastrophic consequences" for using nuclear weapons.
A rash of fires broke out at Russian enlistment centers and government buildings in the wake of Wednesday's partial mobilization announcement.
Video of Chinese tanks "near the Russian border" claimed to be part of strike against "Evil NATO," while others speculated it was a sign of imminent invasion.
Russian President Vladimir Putin has been accused of nuclear saber-rattling by Western leaders.
Russian State TV host Vladimir Solovyov said he was "all for" shooting conscription officers and putting them on the front lines.
Videos posted by Novokuznetsk residents showed clouds of smoke and a bright glow in the area where the steel plant is located.
Zinin's best friend had reportedly been called up to fight in Ukraine as part of Vladimir Putin's partial mobilization.
Military experts say the latest mobilization process "will be ugly, the quality of the reservists poor, and their motivation to fight likely even worse."
Even as the people of Russian-occupied eastern regions of Ukraine "vote" at gunpoint on annexation, the results of President Vladimir Putin's speech last week are playing out.
The governor of the region, Igor Kobzev, said on his Telegram channel that there had been "an emergency" in the area.
"This is the best outcome the Kremlin could hope for," Eleonora Tafuro of the Italian Institute for International Political Studies told Newsweek.
The former NATO commander said the Russian president knows if he used a nuclear weapon "it would cause the world entirely to turn against him."
Videos show women in the Dagestan region of Russia protesting days after the Russian leader ordered countrymen to fight in the war in Ukraine.
National security adviser Jake Sullivan said the Russians "well understand what they would face if they went down that dark road" if nuclear weapons are used.
Queues of people trying to leave the country and avoid being drafted into the army have been seen at the border with Georgia.
Aiden Aslin said he was treated "worse than a dog" during his time as a Russian captive.
Ukrainian forces said two Russian Su-25 jets had been downed alongside a Su-20 and Su-34 plane.
At least 745 people were arrested on Saturday for protesting Russia's mobilization, according to a human rights group.
"They're infuriating people, as if on purpose, as if out of spite," RT's Margarita Simonyan wrote.
Among the unproven rumors circulating is that Li Qiaoming, a general for the People's Liberation Army (PLA), has replaced China's President Xi Jinping.