Yes, the surviving spouse would get a stepped up basis, however on only half the property.
If jointly held the surviving spouse would get a stepped up basis on half the property.
It is important to know if the property was jointly held.
The rules differ for community property states (which Nebraska is not one).
Below is an excellent article on this (it also cites the tax code).
http://www.paelderlaw.com/widows-take-your-step-up-to-reduce-taxes/
