The suspension you suffered will follow you from state to state. There is a slim possibility you could challenge the suspension in California if the DUI law there is significantly different from the law in Nebraska. For instance, if Nebraska has a lower BAL level statute that makes it a lower degree misdemeanor. Most likely though you should just wait out the suspension.
No, all states participate in an Interstate compact whereby they are required to communicate with one another regarding such matters. CA will NOT issue you a CDL until Nebraska is cleared.
John A. Campanella
The consensus is that you will not be able to get a license here in CA until the suspension from NE is cleared. It wouldn't hurt to try if you are here. Also, if you pick up another one here in CA (I know you wont)... you may wish you had challenged the CA use of the NE DUI now. As one attorney pointed out, you may be able to have the CA DMV prevented from using the NE case against you - CA can only use it against you if they are substantially the same offense. One thing we look for, as he suggested, is the BAC level. Some states might make it illegal to have a BAC of .10% while CA is set at .08%. Other differences which are common is the act which is prohibited (CA says driving which requires intentional movement of the car, while other states may only require you to be in control of the car - sitting in it for example). regardless of the fact in your case, the laws may be different enough to prevent the CA DMV from using the NE case agaist you. Fighting it now, rather than after getting a DUI here in CA will be much more likely to bear fruit.