Severance will be taxed just as a bonus would, and the IRS code calls for around 25% to the IRS. Then add the SS and Medicare tax and you will have around 32% off the gross amount. The good thing is that should cover you for the year as far as the tax man goes. I agree with one of the other post about staying on a Chevron with great benefits and a salary. That is better than a year's severance and the govt getting as much as they will. A god job is worth much more than the short-term cash gain. If you qualify for more than a year's pay that makes it a tough decision. People could do a lot worse than work for Chevron, and if they keep the buildings that will be a bonus.
In the end there is going to be a lot more consolidation in the Permian Basin, and the majors are going to have there way. Might as well work for one. I still say one of the biggest issues is health care. A family of four can look to spend upwards of 15K a year for insurance in the market, and Cobra will not be much cheaper, but can be kept for 18 months.