The bill’s approval, coming on the heels of the House passing its own tax bill last month, is the first significant legislative victory for the Republican Party since it assumed control of the House, Senate and White House in 2017. The lightning-fast trajectory of the bill and the ability to overcome — or ignore — objections that have bedeviled previous attempts to revamp the tax code, highlights the pressure Republican leaders faced to notch a victory after several failed legislative efforts this year.

Republicans have pitched the bill as a middle-class tax cut and the overhaul is intended to immediately cut taxes for about 70 percent of middle-class families. But it would raise them on millions of others, since the Senate plan eliminates some tax breaks like the deduction for state and local income taxes and phases out the individual tax cuts at the end of 2025.

Businesses fare far better, with the corporate tax rate cut to 20 percent from 35 percent and made permanent. It also offers a large tax break for the owners of small businesses and other companies that are not organized as traditional corporations, a provision that was sweetened in a last-minute deal to bring two wavering senators on board.

Democrats opposed the tax bill as a bloc, saying it was meant to help the wealthy and not the middle class. With the Senate split 52 to 48, Republicans barely had votes to spare. But the bill’s passage was made possible by a near-complete Republican embrace of the idea that about $1.5 trillion of tax cuts will pay for themselves, by producing enough economic growth and additional federal revenue to offset their costs to the Treasury.

That belief was contradicted by several studies, including one from Congress’s official economic scorekeeper, which Republicans dismissed as overly pessimistic.