$3,000 PFD will raise your federal income tax
If the governor gets the $3,000 Permanent Fund dividend he is demanding (and promises to veto anything less), that means Alaska residents who receive the PFD will owe more federal income tax.
If you are in the 10% bracket and single, that means an extra $300 in income tax. If you are a married couple with no children, it is $600. If you are married with a couple kids, that means $12,000 in income and $1,200 extra in income tax.
You can ask your employer to withhold more income tax from your paycheck starting now. You will need to fill out a new W-4 form — Line 6 is where you show additional withholding. Or you can make estimated tax payments with form 1040-ES available from the IRS website — these are due quarterly.
If you received a large tax refund for 2018 taxes and expect no other changes in gross income, then you should be fine. If you did not, then you should plan now for the increase in your 2019 taxes.