Johnny Carson first and subsequently Jay Leno both appeared to pride themselves on the even-handed nature of their monologues, picking off political targets from both parties, to the point where viewers never knew — by design — where “The Tonight Show” hosts personally stood.

With Jimmy Fallon having replaced Leno this week, the question arises whether he, too, can position himself as the comedic equivalent of Switzerland, especially in these heavily polarized and wildly partisan times, where every aside is pored over and potentially pounced on. As proof, look no further than a piece posted this week by one of Carson’s former writers, arguing that latenight comics were giving President Obama a pass.

Fallon has thus far offered relatively few political jokes in his first week at the “Tonight” helm (he delivered exactly one, a glancing shot at Vice President Joe Biden, in Thursday’s monologue), unless one chooses to count the Russian hockey team being shipped off to Siberia for losing in the Olympics. On Thursday, though, he hosted First Lady Michelle Obama, with whom he previously created a viral-video sensation called “The Evolution of Mom Dancing.”

The latest appearance went a step further, with Mrs. Obama joining Fallon and Will Ferrell in a Nickelodeon parody, even if the skit — pretty awful and interminable — conveniently gave her a chance to promote her children’s fitness message, which was also featured during her interview.

Fallon did gently turn the conversation to the Affordable Care Act, asking why the young people who watch his show should sign up. But that quickly gave way to a lightning round of questions about “firsts” in which the First Lady had participated, which — despite her gameness in playing along — was every bit as dull as that sounds.

Frankly, strictly from a promotional standpoint, hosting the First Lady should be a coup for Fallon in this getting-to-know-you period. Yet given the deep-seated antipathy toward the Obama administration in certain precincts, even non-controversial campaigns associated with the administration — such as the First Lady’s initiative trying to get kids to eat better and exercise more — have triggered attacks from conservative media figures.

Either way, Fallon is going to be closely watched for signs of his politics — especially with David Letterman having dispensed with any pretense of impartiality, expressing thinly veiled disdain for the current state of the Republican Party (and Sarah Palin in particular); and “The Daily Show’s” Jon Stewart (while hardly giving Obama a free ride) invariably more likely to skew conservatives.

Fallon’s opening frame has characterized him as a pretty innocuous host in that regard, one who seems committed to being on good terms with everybody. As for whether that can continue in today’s environment, well, let’s just say he had better keep brushing up on his dancing skills.