I personally don't know of any CCW person here that purposely breaks the law by carrying into a signed business. We are not about compromising our rights by breaking the law.
So, Yes, the sign has the force of law in Nebraska
If a person, persons, entity, or entities in control of the property or an employer in control of the property prohibits a permit holder from carrying a concealed handgun into or onto the place or premises and such place or premises are open to the public, a permit holder does not violate this section unless the person, persons, entity, or entities in control of the property or employer in control of the property has posted conspicuous notice that carrying a concealed handgun is prohibited in or on the place or premises or has made a request, directly or through an authorized representative or management personnel, that the permit holder remove the concealed handgun from the place or premises. A permit holder carrying a concealed handgun in a vehicle into or onto any place or premises does not violate this section so long as the handgun is not removed from the vehicle while the vehicle is in or on the place or premises. An employer may prohibit employees or other persons who are permit holders from carrying concealed handguns in vehicles owned by the employer.