Hey, if it's good enough for them,

it's good enough for me.
A search of the Nexis database shows four recent examples of Heilemann using "regime" to refer not to tyrannies but to American domestic politics. He even used the phrase "Obama regime." For the record:

In the January 19, 2009 issue of New York, Heilemann wrote that Barack Obama had no particular expertise in economics, "So it's ironic, to say the least, that the first defining moment of the Obama regime happens to revolve around matters macroeconomic -- dealing not just with a nasty and potentially prolonged downturn, but with a wrenching, epochal crisis of capitalism on a global scale."

In the January 5, 2009 issue of New York, Heilemann wrote of "the power troika of Bob Gates, Jim Jones, and Hillary Clinton, each of whom plausibly could have filled the very same jobs in a John McCain regime."