I am a contract worker who has worked and lived out of state for just over a year. I have received a per diem of 2/3's of hourly pay rate for my out of state living expenses. The W-2 that I received only reports the 1/3 that was taxed. I am responsible to pay federal tax on the per diem?

The IRS considers it taxable after one year (unless you expected the time away from home to be less and it ran over, not sure how they want you to prove that).
BUT I wonder why your employer didn't report it? Have you asked them?

Per diem is not taxable IF it meets certain rules. As joy says - if may be tax-free for up to one year, but there are also other rules regarding the amount that you may be paid as a per diem and for what purpose without it being taxed. That amount depends on where your job assignment is. So tell us where you work and we can tell you ho much the per diem is allowed to be and remain untaxed.