If the client is paying above average or giving you what you consider a very valuable opportunity, consider hiring your own lawyer to review the document.
If the client is paying a normal rate and/or if you believe that your skills are in demand, consider increasing your rate for the added cost of reviewing the NDA and complying with its terms.
If you have professional friends or colleagues, show them the NDA first. At a glance, those friends may pick up terms that are really disadvantageous to you or that are overly broad. And while this doesn't replace an actual lawyer reviewing those terms. It may help for an initial first pass.
For an initial first pass, you may even want to extract a few snippets of key phrases, surround them with double-quotes, and do a google search on each one of them.
And yes, ask the company to give you the key highlights. That's part of it too, but that's not the only thing you should do since you certainly can not trust what they tell you. If the person tells you that a clause won't be enforced or that it doesn't apply to you, I'd suggest you strike that clause out yourself (either that or replace it with what they told you it meant), and ask the other party to initial and sign the changes. Note that this may only work with smaller companies or eager companies that really want to hire you.
And if there is a non-compete in there, make sure that the non-compete has a short expiration date and that you get adequately compensated for its full duration. In other words, make sure that you are compensated for any and every little thing that is out of the ordinary and that they demand from you. By being diligent now, you're not only protecting yourself but you're also protecting your future clients from being part of a lawsuit they have no desire to be part of.
In the meantime, keep on looking for other work, because they may just balk and walk away, or you may just balk and walk away yourself.