Would you say that in this financial climate it is not a good idea to ask for a severance package when negotiating a new contract for a new job being offered?

Most companies won't  negotiate that   unless  you are a C-level employee.    However....

If a company wants you badly for a job (i.e.  you have a niche skill-set that is in high-demand, you can always say, "I am happy  where I am right now and know I have long-term  employment here.  Thus, leaving would  require me to have some sort of severance  agreement to ensure that if I was let go unexpectedly, I would have time to look for a new opportunity sufficiently."  This may or may not work, but it doesn't hurt to ask.

Otherwise, you most likely will be turned down if you ask for a severance agreement - especially, in this economy. A company would fear getting burned and won't want to risk having to pay an employee extra money to let them go because they weren't a fit. I realize the employee is always at risk of getting burned too, but with at-will employment, we are all businesses-of-one who's #1 client (employer) can stop using us at any time.

This all goes back to the importance of figuring out what our 'go-to potential' is and leveraging it so we become a sought-after expert in our
area of expertise. This ties to the personal branding concept. Build a strong brand and you can ask for things like severance!

J.T. O'Donnell, Founder & President of Careerealism