The full bill was released Thursday morning. President Donald Trump touted this as "the biggest tax event in the history of our country" on Tuesday.
"Nothing is easy, however, and there is still tension over what tax provisions can be limited or eliminated to offset aggressive cuts in marginal corporate and personal rates. A balance will need to be struck," Steve Blitz, chief U.S. economist at TS Lombard, said in a note.
The increasing prospects of tax reform have recently helped U.S. stocks reach record levels.
Phil Blancato, CEO of Ladenburg Thalmann Asset Management, said "the market still doesn't believe tax reform will get done this year," however. "There are too many Senate Republicans that are not behind this plan."
Top White House economic advisor Gary Cohn said Trump would support the bill so long as it preserves key elements.
Investors also saw Trump nominate Fed Governor Jerome Powell to become the central bank's next chair. Powell's nomination was widely expected by experts and most investors.
"Powell is dovish. The current Fed chair, Janet Yellen, is dovish. I think the market has priced in a dovish Fed chair," said Adam Sarhan, CEO of 50 Park Investments. "Central banks are slowly raising rates, but they are still very low relative to historical levels."
If confirmed, Powell would replace Yellen, who took over as Fed chair in 2014.
"While it is expected that he will continue the gradual path towards rate normalization, there are questions regarding his views on the continuing de-regulation of the financial industry," said Quincy Krosby, chief market strategist at Prudential Financial, in a note. "Under Powell expect a pragmatic path on monetary policy, along with an equally pragmatic path on industry regulation. In other words, continuity with a Republican tilt."
Wall Street also kept an eye on earnings after tech giant Facebook posted better-than-expected quarterly results. Facebook reported adjusted earnings per share of $1.59, well above the expected $1.28.
Companies set to report Thursday after the bell include Apple, Starbucks and CBS.
Overall, earnings have mostly outperformed expectations this season, adding to the stock market's already strong gains for the year. As of Thursday morning, nearly 73 percent of the companies that have reported have surpassed earnings expectations, according to Thomson Reuters I/B/E/S.
—CNBC's Patti Domm contributed to this report.