What does one's status being “less a blank check than an equation with multiple variables” mean?

In this case, "less A than B" (where A is "a blank check" and B is "an equation with multiple variables"), means that there's two ways you could describe something, but that the first way isn't as accurate as the second.

You can also say "not so much A as B".

http://q.hatena.ne.jp/1124350498 (I didn't deliberately choose a Japanese language website - google is under the delusion that I can read Japanese!) has an example of this with "He is not so much smart as clever." - in that case, you could be tempted to describe that person as smart, but clever would be a more accurate description.

A blank check is a personal check that's signed and ready to (turn into) cash, except for the amount of the check: that has been left blank, so the beneficiary of the check (the one who gets to cash it at the bank) is allowed to fill in the amount. Politically, this would mean that Hillary Clinton is the guaranteed nominee in 2016, but because she doesn't have a blank check, she isn't guaranteed the nomination.

The phrase "her next few years are an equation with multiple variables" means that her fitness as a candidate for the presidency will finally be determined based on a few things (the multiple variables). If the solution to that equation is higher than the solutions to the equations of other contender's equations in 2016, she'll probably be nominated.

Her status is singular but complicated is important for understanding the check/equation metaphors. She's the most popular American politician at the moment and if there were a Democratic primary tomorrow, she would win hands down (in a landslide) -- which makes her status singular -- but it's also complicated for a variety of reasons, past and present -- which is why there are multiple variables in the equation for deciding who will be the 2016 nominee.