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Since Republicans are using a legislative process known as reconciliation - meaning they can push a bill through Congress without any support from Democrats - they must keep the cost of the bill to $1.5 trillion over 10 years.

The Senate bill would fully repeal the state and local deduction claimed by many taxpayers, an idea that has drawn vigorous opposition from House Republicans in NY and New Jersey and resulted in a compromise in the House version of the bill that would allow property taxes to be deducted up to $10,000. The House's version, meanwhile, only limits the deduction.

Both bills propose lowering corporate tax rates, increasing the standard deduction for individuals, removing numerous current tax deductions, and encouraging USA companies to bring back revenues parked overseas.

Republicans in the Senate would likely not pay the same political price since the high-tax states primarily have Democratic senators.

The tax bill must deepen federal deficits by no more than $1.5 trillion over the coming decade.

The House version would collapse the current seven tax brackets into four, while the Senate would retain seven. On this point, House leaders have taken on an impossible task.

She noted that Republicans from the likes of New York, New Jersey and California were unlikely to vote for a bill that brought about a complete repeal of deductions on state and local taxes, and that while not a deal-breaker, several other representatives would be opposed to any delays to corporate tax cuts. This targets firms like U.S. pharmaceutical companies who file patents for drugs overseas and book the profits for those drugs in lower-taxed companies. While 1.6 million households in New Jersey claim the property tax deduction today, that number is expected to fall by almost 60 percent next year, to just 650,000, under the House bill. The threshold for an estate to qualify, however, is immediately doubled. It creates a new 38.5 percent tax bracket for couples earning more than $1 million and individuals making more than $500,000 per year.

Yet as the Senate Finance Committee unveiled its bill, a few stark differences emerged with the version approved by the House tax-writing committee, underscoring the challenges ahead in getting both chambers to agree on the complex and far-reaching legislation that would affect almost every American.

Using the ITEP Microsimulation Tax Model, we calculate that almost 1 million New Jersey households would no longer receive the property tax deduction if the House bill is enacted. The House's proposed cut caused an uproar from homebuilder and realtor groups.

Despite having property taxes that could potentially be deducted under the House bill, many of these taxpayers would not deduct those taxes in practice because the combination of itemized deductions they are allowed to deduct (which would no longer include state income and sales taxes) would be smaller than the standard deduction. The Senate bill keeps both of those credits, sidestepping those issues.

The House is expected to vote on its tax measure next week.

The House and Senate bills are broadly similar in their outlines.