WASHINGTON >> The Senate today barreled toward the most sweeping rewrite of the tax code in more than three decades as the top Republican senator said he was willing to compromise on a major sticking point for lawmakers from high-tax states such as New York and California.

The Senate voted 51-47 to formally begin negotiations with the House in an effort to reconcile their two tax bills. Days and nights of tough negotiations await.

GOP leaders are pushing to send a final blended package to President Donald Trump to sign before Christmas. Republicans see the tax overhaul as a pressing political imperative to preserve their majorities in Congress in next year’s elections.

“The American people deserve taxes that are lower, simpler and fairer,” said Senate Majority Leader Mitch McConnell, R-Ky. “By voting to go to conference, we will be one step closer to getting it done.”

Before the Senate vote, McConnell said he favors expanding a deduction for state and local taxes to enable Americans to deduct local income taxes as well as property taxes.

The proposal is a possible solution to a standoff with rebellious House Republicans from high-tax states. The tax bills passed by the House and Senate would end deductions for state and local income and sales taxes, while allowing only a deduction of up to $10,000 for property taxes.

Several GOP lawmakers from high-tax states voted against the House bill last month.

“The state and local tax deduction is not as important to Senate Republicans as it is to House Republicans,” McConnell said on the Hugh Hewitt radio show.

“There’s some in the House who would like to see that applied not just to property, but to income tax, you know, where you can sort of pick which state and local tax you want to deduct,” McConnell said. “That sounds like a kind of reasonable idea.”

The House and Senate bills both would provide steep tax cuts for businesses and more modest tax breaks for families and individuals. The tax cuts in each bill add up to about $1.5 trillion over the next decade.

Rep. Kevin Brady, R-Texas, said negotiators are looking at several options to help people who live in high-tax states, including expanding the state and local tax deduction to include income taxes.

“That’s one of the options that our lawmakers have brought to us from California and New York and Illinois and others. So yes, we are looking at it,” said Brady, who is one of the lead negotiators for House Republicans.

Brady said lawmakers are also considering adjusting the tax rates, adjusting the tax brackets, increasing the child tax credit and eliminating the alternative minimum tax, which was intended to ensure that high-earners pay at least some tax.

The House package eliminates the AMT; the Senate bill reduces the number of people who would pay it.

The House bill increases the child tax credit from $1,000 per child to $1,600; the Senate bill increases it to $2,000.

Associated Press writer Alan Fram contributed to this report.