The Senate narrowly passed Republicans' tax reform legislation early Saturday morning with no Democratic support, following a marathon voting session overnight.

The bill, approved just before 2 a.m. in a 51-49 vote, next heads to conference, where House and Senate negotiators will work out the differences in their bills. Sen. Bob Corker (R-Tenn.) was the only Republican to vote no on the measure. The House bill also passed with no Democratic support last month.

The legislation was officially released shortly before the vote, giving the public little time to examine the final details. Democrats were outraged, asking for more time to review the measure. Sen. Claire McCaskill (D-Mo.) claimed she was handed the amendments to be included in the bill not by any of her colleagues, but by a lobbyist. Lobbyists, her comment implied, saw the bill before Democratic members.

Last-minute tax plan

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"Not a single member of this chamber has read the bill," Senate Minority Leader Chuck Schumer (D-N.Y.) said on the Senate floor before the bill passed. "It would be impossible."

Senate Majority Leader Mitch McConnell, who held a press conference after the bill's passage, suggested Democrats were only concerned about the legislative process because they were losing.

"You complain about process when you're losing," McConnell said. "And that's what you heard on the floor tonight."

McConnell also said he believes the bill will be revenue neutral, despite analyses suggesting it will add to the deficit.

"This is a great day for the country, it's been 31 years since we've done comprehensive tax reform," McConnell said.

President Trump hailed the bill's passage in a tweet Saturday morning, thanking Republicans for approving the measure.

Biggest Tax Bill and Tax Cuts in history just passed in the Senate. Now these great Republicans will be going for final passage. Thank you to House and Senate Republicans for your hard work and commitment! — Donald J. Trump (@realDonaldTrump) December 2, 2017

The Senate bill permanently lowers the corporate tax rate from 35 percent to 20 percent. Tax rates will also be cut for individuals, though their tax cuts will expire after a decade. The Senate bill keeps the same number of individual tax brackets, although it changes what those brackets are.

The Senate bill also repeals the individual mandate under Obamacare, something conservatives in Congress have long wanted. The House version does not touch the individual mandate.

The Senate bill, like the House bill, limits state and local income tax deductions to property taxes, with a cap of $10,000. The Senate bill increases the child tax credit from $1,000 to $2,000.

Republicans -- with the help of a tie-breaking vote from Vice President Mike Pence -- approved a provision from Sen. Ted Cruz, R-Texas, that expands a tax break for 529 contributions to K-12 schools. The Senate shot down an amendment From Sens. Marco Rubio, R-Florida, and Mike Lee, R-Utah, to further expand the child tax credit in exchange for a corporate tax rate increase from 20 percent to just under 21 percent.

The Senate bill is expected to add more than $1 trillion to the deficit over the next 10 years, according to a Joint Committee on Taxation analysis. Republicans had hoped the bill would pay for itself, and there was some concern late Thursday the bill would be held up for fiscal reasons.

The bill's passage is a major accomplishment for Republicans, who have been unable to pass significant or complex legislation since they took control of the House, Senate and White House in January.

CBS News' Alan He contributed to this report.