I collected about 15000 in unemployment last year while being a resident of New Yorks state and had no other source of income. Using turbo tax, my federal tax owed was quite high but my taxes owed to New York state were calculated a $0. Is this wrong? Is unemployment a federal program only? I figured I would owe a large amount to both.

Any unemployment compensation you receive is subject to Federal,NYS and Local income taxes if you are required to file a tax return.However, as you know, under current legislation, the first $2400 of unemployment benefit payments paid in 2009 are exempt from your federal and State taxes.
For example, last year, you collected $15,000 for your UIcompensation and your Federal marginal tax rate is 25%, then $15,000-$2,400=$12,600*0.25=$3,150 is tax.So your net UI compensation amount is $15,000-$3,150=11,850 after paing your Federal tax on the compensation.You also should pay State or local level taxes on it.