WASHINGTON — Senate Republicans, under pressure to pass a sweeping tax rewrite before year’s end, are expected to unveil legislation on Thursday that would eliminate the ability of people to deduct state and local taxes but would stop short of fully repealing the estate tax, according to lobbyists and other people familiar with the bill.

The Senate plan is taking shape as Republicans digest the drubbing they suffered on Tuesday night in affluent suburbs across the country, many of them represented by Republicans in the House. Those areas are stocked with well-off voters who would be disproportionately hit by the elimination of state and local tax deductions.

But in the Senate, those high-tax areas are often represented by Democrats, which puts less pressure on Republican leaders to keep the state and local deduction, in any form, in their version of the bill.

Each of the bills reflects delicate political and fiscal calculations as Republican leaders seek to deliver on President Trump’s campaign promises to cut taxes on the middle class and on businesses — but also find the money to pay for them. Eliminating the state and local tax deduction would increase tax receipts and therefore lessen the overall cost of the legislation, which by congressional budget rules cannot exceed $1.5 trillion over the next decade if it is to pass without Democratic support.