What about private loan consolidation?

It's not a bad idea to consolidate your private student loans. What is a bad idea is combining federal and private student loans, which results in a consolidated private loan. This is bad for many reasons:
You cannot defer payments on a private loan consolidation if you want to go back to school. You can with federal loan consolidation.
You cannot forbear payments in case of economic hardship on a private loan consolidation.
You cannot claim interest as a tax deduction on a private loan consolidation.
You cannot apply for forgiveness on a private loan consolidation. Certain types of work, such as federal volunteer programs, teaching in economic development zones, and military service, among others, can qualify you to have part or all of your federal loans dismissed by the government.
If you should pass away, private loans are passed to your next of kin. Federal loans are forgiven.
Private loan consolidation very often has variable rates, which means you cannot lock in today's current historic low rates. Those rates may be tied to volatile indexes like the Prime Rate, which can jump as high as 13%.

Consolidating your federal student loans first is very important, because in doing so, you reduce the number of open lines of credit (loans) you have. This boosts your credit score, enabling you to obtain better terms for private loan consolidation.