I work as a contractor in NC but live in SC. Do I need to pay estimated taxes to both states? Or just one? Or can I have my husband take extra withholding from his job?

Since your work income is taxable by NC, you should definitely pay estimated taxes to NC.

It is also taxable by SC (your home state can tax all your income), but you'll be able to claim a credit on your SC return for the taxes paid to NC.  The credit will likely cover only a portion of your SC tax bill, since SC's income tax rate is a bit higher than NC's. 

If your husband works in SC, an increase in his state withholding would help.  This would be easier than paying estimated taxes to SC.

Wonderful, thank you for your help! Yes, my husband works in South Carolina, so having him increase his state withholding seems like a good way to go.