What happens if I cannot pay my State taxes for a year?

Can I make up for it next year? When I bought my house this year, I had to liquidate my mutual fund savings and I am going to get grilled on taxes because of the extra income. I can afford the $3000 I owe for Federal, but cannot afford the $1200 state at this time.

I am exactly in the same boat as you. But for alot more money. My tax adviser says the IRS gives you up to three years to pay federal. You must send them a form asking for an extension though.
In short if I were you I would go ahead and pay the state and hold off on the federal for a while.

Enter in to an installment agreement with them and pay it off a bit each month.

Do not just let it go for a year. That $1200 will turn in to $2000+ before you know it.

Set up a payment plan with the state. You can't just ignore it entirely--or you can, but you will have to deal with the consequences. Pay them every month, but you need to pay them something by 4/15 to start your plan. You will face penalties and interest, meaning the amount you owe will grow significantly. Better to deal with it than to ignore it until next year. Next year, could be turned over to collection agency, could be grabbed from federal refund, etc.

put it on a credit card or make payments to the IRS as long as they see you are trying you will be ok

You can pay it later. However, you are going to be charged interest and penalties for the amount that goes unpaid. Also, several states have actually gone to using collection agencies. This means that they will turn it over to a CA and the CA will place a listing on your credit report.

The best thing to do is contact your State's tax office and see if you can work out a payment plan. This could avoid the penalties and being turned over to a collection agency.

My suggestion? Pay at least SOME amount on both.

Say...$120 on the state, and all but $120 on the Federal...just as an example.

I'm not sure about the state taxes, but you can set up payments with the IRS for your federal return. In fact, that's what I have to do this year. I thought that by paying full taxes on my side jobs, I'd have just enough to pay taxes on my regular job. I was wrong--next year, I'll just switch that up.

You'll be charged a penalty fee. Not sure how much that is.