There's been a federal income tax for over 100 years and the nation hasn't collapsed and the wealthy appear to be doing just fine.  
But adding a state sales tax into the mix somewhere seems reasonable.  If so, make it a seasonal tax - 1 May to 30 September.  Exclude essentials such as medicine, residential utilities, and unprepared food.  Maybe as a compromise both need to be added.  
BUT...add a clause that ratchets the tax rates down as oil revenue goes up.  If the price of oil rises or that mythical new production comes online, taxes go down.