Indeed, Alaska's rich natural resources and wealth actually pay dividends to residents, Walker said, a payment some have suggested should be eliminated from the budget. But those in rural and low-income areas still need that to offset energy costs, thus the tax, Walker said.
"The income tax itself brings in $200 million for a $3.5 billion problem, so it's not the biggest lever we're pulling at all," Walker said. "It's one of many that we're looking at making some adjustments [to]."
Also on the table are $100 million in additional cuts from the operating budget and $425 million in cuts from oil exploration credits, according to the governor's website.
The move has been politically unpopular, with critics questioning whether it hurts Alaska's competitiveness for business. But even with the new tax, Walker said Alaska still have one of the lowest personal tax rates in the nation.
"I don't believe our doing what other states have done at a very low level ... is going to drive anyone out of the state or keep anyone from coming in to the state," Walker said. "We're just trying to look more like other states, in some respects."
— CNBC's Christopher Hayes contributed to this report.