Ms. Brown, a Democrat, said repealing the deduction will put pressure on state officials to reduce taxes at a time when Oregon is already fiscally stretched in providing education, law enforcement and other services to its residents.

“We are already struggling to pay for basic services,” said Ms. Brown, who acknowledges that her team has not been able to fully analyze the scope of the legislation because it has been moving and changing so rapidly. “For Congress to move so quickly on a ginormous tax policy like this that has extremely far-reaching impact is just crazy.”

Such worries are widespread and they come at a time when state budgets are being squeezed despite a steady economic upturn nationally. Economists attribute the shortfalls to a mix of slower sales tax revenues and ill-advised tax cuts in some states combined with a hangover from the recession. The Trump administration has also called for budget cuts that would put more responsibility on the states to provide for their residents. And overhauls to welfare programs such as Medicare and Medicaid could follow if Republicans succeed in cutting taxes.

The full repeal of the deduction, often referred to by its acronym, SALT, is not a foregone conclusion. Senate Republicans want to eliminate it completely, saving about $1.3 trillion over a decade, while House Republicans have agreed to maintain a deduction for up to $10,000 in property taxes. The two plans ultimately must be aligned before legislation can be passed and sent to President Trump’s desk for signing.

The Trump administration and most Republicans in Congress make the case that the state and local deduction is an unfair subsidy for high tax states that burdens both the federal government and other states with lower taxes. They also contend that it overwhelmingly benefits wealthy taxpayers that are concentrated in a handful of states that are mostly led by Democrats.

With a Trump administration that is filled with wealthy New Yorkers, the White House is keenly aware of these concerns, and Steven Mnuchin, the Treasury secretary, has expressed openness to compromise on the issue. Noting that he has lived in both California and New York, which would be among the hardest hit by a repeal, Mr. Mnuchin has said he is sensitive to the broader impact on the nation of policies that might stunt the growth of state economies.

Many leaders in New York hope that the members of the Trump administration who hail from the state will intervene. Some have even appealed to Mr. Trump’s sense of self-interest, warning that getting rid of the deductibility of local taxes could be a big drag on the value of the president’s condominium business in Manhattan if people can no longer afford to live in them.