To sleep your way to the top

Question

He was insinuating that she slept her way to the top.

Most memorably, Huffington urges the assembled luncheon group: “Sleep your way to the top. Four hours is not enough.” She is a big advocate of naps and of dreaming up ways to reshape the workplace that men have designed.

What does it mean?

As I see it, you either don't get to the top because you like to sleep a lot; or you get to the top through beds (fornicating).

EDIT:

I found this TED video where Arianna Huffington uses this idiom in a funny way.

Answer 1

It's intended as a form of wordplay. As the comments note, to sleep one's way to the top is an idiom that means the trading of sexual favours for advancement of some sort. Although it can be applied to both sexes, it is usually an insult leveled at women who, correctly or not, are perceived as being unqualified for the positions they hold. (The stereotypical unqualified secretary, for instance.)

Given this context, the phrase can be seen as empowering for women who nap to increase their productivity. Stated plainly, it would be something like this:

You know how they say you only got where you are because you slept your way there? Well, you know they're wrong in terms of sexual favours, but make it a literal reality. Sleep more. Be more productive with a nap. Turn the insult into personal betterment.

The context includes "workplaces men have designed", so it's fairly clear that Huffington intends for her listeners to pick up the double meaning. She's basically saying, "Take that insult, embrace it, and make it backfire."

In some ways, it can be seen as analogous to the old joke:

Three men walked into a bar. Two were fine, but one had to have stitches.

You expect one thing from the sentence, and then when the full context is given, there's a shift in your perceptions. Huffington is doing the same thing with the phrase "sleep your way to the top".

Answer 2

Both of your interpretations are correct. The first example you provide is generally understood as a euphemism describing promotion up through the ranks achieved by plying superiors with intercourse.

The second example is a reference to the first with an alternate meaning suggested. It may help to know that Arianna Huffington is known for her unique manner of speaking (you might have seen her lampooned on SNL by Nasim Pedrad) and is often a bit cheeky or provocative in getting her point across. During her recent appearance on The Daily Show, she presented her new book of advice and discussed her implementation of these practices in her management of the offices of The Huffington Post in the form of nap rooms for employees:

The other day I was walking by and I saw two people walking out of one of the nap rooms. I thought “Hey, whatever it takes to recharge.”
_{Source: Video clip of The Daily Show – Interview with Arianna Huffington on March 24, 2014}

The usage of “sleep [one's] way to the top” in its usual sense is generally applied to a woman who holds high rank in a company, and it is a way of dismissing her accomplishments or merit and asserting that the only way she could have achieved that position is by prostitutional bartering. It's euphemistic nature and ubiquity make it a good example of microagression, but I have the sense that its use will continue to wane as this sort of personal derogation (even in euphemism) finds less acceptance in society.

Her intentional twisting of this phrase's meaning is well in line with the theme of the advice she is giving in the process to reject the premises of workplace sexism. She often speaks of a revolution of sorts that will redefine success, especially for women operating in a professional atmosphere where success has traditionally been defined by men. In the commencement speech she gave to 2013 graduates of Smith College (a women's university), she referred to that college's president's speech nine years prior:

In 2004, President Christ gave a speech that was really ahead of its time. It was titled "Inside the Clockwork of Women's Careers." To me, it's very much a third women's revolution call to arms. She spoke of the need to dispel myths about ambition and success, chief among them the myth that success and ambition look like a straight line. Now I guess it's no big surprise that the image of success created by men would be, yes, a long, phallic-shaped line.
_{Source: Huffington Post – Arianna Huffington's Smith College Commencement Speech On Redefining Success: The Third Metric}