With the Democratic race heating up and much of the mainstream media starting to admit that Bernie Sanders is a serious contender, the pressure is on for front runner Hillary Clinton to distinguish herself from her challenger.

She made a go at it today by criticizing Bernie Sanders's college plan, which would offer tuition-free higher education at America's public colleges to all students. As Politico reports, Clinton said she didn't want to make college “free for Donald Trump's kids.”

"Now, I'm a little different from those who say 'free college for everybody.' I am not in favor of making college free for Donald Trump's kids. I am in favor of making college free for your grandson by having no-debt tuition," Clinton told an undecided 71-year-old voter identified as Candy during the event, which was broadcast live Monday on NBC's "Today."

There are a few things to say about this, but to start with, Clinton's example is a straw man. “Hillary Clinton needs to take a good hard look at where people like Trump send their kids to college. They go to private schools,” Sara Goldrick-Rab, a higher education expert at the University of Wisconsin-Madison, told Alternet. Sanders's proposal only offers tuition-free college to students at public universities — everything from the City University of New York to the University of Georgia.

Here's where Trump's kids went to school:

Ivanka Trump: Ivanka went to Georgetown and then the Wharton School at the University of Pennsylvania, both private schools.

Eric Trump: Eric went to Georgetown.

Tiffany Trump: Tiffany goes to UPenn, like her sister Ivanka did.

Donald Trump, Jr.: Junior also went to Upenn.

Barron Trump: Barron is 9 years old and therefore has not gone to college yet.

But the greater point here is that Clinton seems set on making higher education a means-tested welfare program. Imagine if someone were to argue that we should only pay for K-12 education or police for children up to a certain income level; for years, progressives have resisted such income caps on programs like Social Security and Medicare, arguing that universality is important as a principle, both in and of itself and for political reasons. After all, wealthier people are much more likely to support programs if they benefit from them as well.

And there are only 500-something billionaires in the United States. If they decided to stop sending their kids to elite private schools and instead opted for sending them to public colleges, we're talking about a handful of families, not exactly a huge drain on the public treasury. Especially when you consider the fact that education is a public investment that pays for itself.

“Free college is about the public sector, and it's very well-targeted to where the need really is. Frankly, if Hillary is knocking free college, then Bernie must be doing something right,” says Goldrick-Rab.