In the rare event that an American politician made the effort to use Russian, it would probably sound like Sean Connery speaking поу-рашшшки in The Hunt for Red October, though minus the Scottish accent.
If we were EXTREMELY lucky, it might sound like Sam Neill speaking Russian in The Hunt for Red October. (Neill obviously spent time practicing with a dialect coach, and as a result his Russian was "less worse" than Connery's -- Connery didn't even try.)
P.S. Vitaly Mutko's speech also reminded me a little bit of the Мульт Личности version of President Obama -- the озвучение was done, of course, by a Russian actor pretending to have a heavy American accent, and not by an actual American actor!