NEW YORK — Democrats in high-cost, high-tax states are plotting ways to do what their states’ representatives in Congress could not: Blunt the effect of the newly passed Republican tax overhaul.

Governors and legislative leaders in New York, California, and other states are considering legal challenges to elements of the law that they say unfairly single out parts of the country.

They also are looking at ways of raising revenue that are not penalized by the new law. And they are considering changing their state tax codes in ways that would let residents take advantage of other federal tax breaks — in effect, restoring deductions that the tax law scaled back.

Philip D. Murphy, a Democrat who will be sworn in as governor of New Jersey in January, has said his administration might challenge the law on constitutional grounds. Democrats in other states have made similar suggestions.

Legal scholars said states could try to argue that the law treated certain states unfairly. They might also argue that the 16th Amendment, which authorized the federal income tax, meant to define “income’’ as income after state taxes had been paid, essentially enshrining the state and local tax deduction in the Constitution.

One legislative proposal would replace state income taxes, which are no longer fully deductible under the new law, with payroll taxes on employers, which are deductible. Another idea would be to allow residents to replace their state income tax payments with tax-deductible charitable contributions to their states.

Such ideas may sound far-fetched. And until recently, they were mostly the province of tax professors and bloggers. But they are now getting serious consideration in state capitols where governors and legislators see the Republican law as a thinly veiled assault on parts of the country that typically vote for Democrats.

Companies, of course, have long sought to exploit loopholes in the tax code. Governments, as a rule, have not. State leaders, however, said Congress, in singling out certain states, had broken an implicit compact with the states.

“The game has changed,’’ said state Senator Stephen M. Sweeney, the Democratic president of New Jersey’s Senate. “They’ve completely turned the tables against us.’’

In particular, officials in the high-tax states object to the law’s $10,000 cap on state and local tax deductions, which were previously unlimited. That provision will be particularly painful for residents of states like New York, New Jersey, California, and Connecticut, which have high housing costs and high tax rates.

Even in those states, most residents will get a temporary tax cut because of other provisions of the law, including lower tax rates and an increase in the standard deduction.

But the cap on the state and local tax deduction could pose a serious threat to state budgets, because it makes state taxes more expensive for residents. That could make it harder for states to raise taxes, particularly on wealthy residents, and could increase pressure to cut spending.

The law could also have broader economic consequences. Business leaders, for example, have said they worry about attracting workers if New York and other cities become even more expensive than lower-tax areas.

State leaders are still figuring out their response to the new law, and few have yet endorsed specific proposals. But they are moving quickly. Governor Andrew M. Cuomo of New York, a Democrat, recently said he expects to provide a more detailed plan soon.

“They want to target us for certain provisions?’’ Cuomo asked at a recent news conference. “Well, let’s see if we can redesign our tax code to get out of the federal trap that they set.’’