Reviewing the absurd-looking 2016, Kevin Drum says the film shows "Daniel Pipes, who thinks Obama hangs out with Israel-haters and would show his true anti-Zionist colors if were reelected."
Pipes and Israel aside, I find that there's a weirdly persistence to the view that this general kind of thing is possible. In other words that once re-elected, a president will find himself unleashed from the chains of the Median Voter Theorem and able to pursue his "true" extreme agenda. And yet there are basically no examples of this happening. Nothing especially right-wing occurred in the second terms of Dwight Eisenhower, Richard Nixon, Ronald Reagan, or George W Bush and nothing especially left-wing happened in Bill Clinton's second term. The exception that proves the rule here is that Lyndon Johnson's second term saw a lot of liberal legislation. But 1964 was Johnson's first electoral win and he wasn't constrained by the constitution from running for re-election.
And the reason this doesn't happen is pretty clear—Congress.
It's virtually never the case that the sitting president is restraining an own-party Congress from passing ideologically extreme measures that he secretly favors and will be able to endorse after his re-election. If Obama is re-elected then he's not going to curtail aid to Israel because even if he wanted to, Congress won't agree. In fact, if Obama is re-elected it's very likely he'll be facing a Republican Congress and thus that are options are either that basically no legislation will pass or else that some kind of high-minded centrist bills will happen. That's how America works.