New York Governor Andrew Cuomo announced that New York, New Jersey, and Connecticut are suing the federal government over the GOP tax bill, specifically over the provision that added a $10,000 limit on state and local tax deductions. High-tax states often perceive this as an effective increase on their residents' tax burden.

Why it matters: This is the latest in a series of pitches many blue, high-tax states have been launching to try and bypass the new requirements.

Repealing income taxes and replacing them with payroll taxes on the employer-side could look attractive to high-tax states since payroll taxes are still deductible, Vox’s Dylan Matthews notes. New York’s Department of Taxation and Finance proposed a program like this earlier this month, per CNBC.

• The downside: This method doesn’t address all income types, including capital gains and investments.

Residents could donate money to their state governments, and in turn state governments could provide them tax credits for the charitable contributions. This would act as a credit against their state income tax payments since charitable contributions are still deductible, the NYT’s Ben Casselman points out. There are proposals like this circulating in California and New York right now, per CNBC.

• The downside: Jared Walczak, senior policy analyst at the Tax Foundation, told CNBC: "These [existing program] contributions produced an actual charitable benefit, whereas the proposals involve a pure tax swap…The IRS requires that charitable contributions have genuine charitable intent and a charitable outcome."

States are also considering shifting more taxes to corporations and away from individuals, per the NYT.

• New sources of revenue are starting to look attractive to states as well, such as legalizing and taxing marijuana.

One final strategy blue states could employ to avoid the changes to state and local taxes: Winning back Congress.