Trump says people will be 'very, very happy' with Republicans' tax overhaul The Senate passed the bill by 51-49.

 -- President Donald Trump praised the Senate's passage of the Republicans' massive tax overall, saying people are going to be 'very, very happy' with the law.

Now that the Senate passed its bill, the next step is for the House to vote Monday to send its tax legislation to conference committee. At some point next week, the Senate will do the same thing, and then they will begin merging the two bills in conference.

"Something beautiful is going to come out of that mixer," Trump said Saturday morning of the Senate and House conference process. "People are going to be very, very happy. They're going to get tremendous, tremendous tax cuts and tax relief and that's what this country needs."

Senate Republicans passed their version of the tax overhaul by 51-49, marking a significant victory for the GOP and Trump. It also marks the first major overhaul of the U.S. tax system in 30 years.

No Democrat voted in favor of the legislation.

Tennessee Sen. Bob Corker, a Republican, joined Democrats in opposing the bill.

The bulk of the bill's tax cuts affect businesses and higher-earning individuals and gives more modest breaks to others.

"I commend my Senate colleagues for this historic action," House Speaker Paul Ryan, R-Wisc., said in a statement following the passage of the Tax Cuts and Jobs Act. "For the first time since 1986, both the House and the Senate have passed a major overhaul of our nation’s tax code. Now we will move quickly to a conference committee so we can get a final bill to President Trump’s desk."

Ryan continued, "The hardworking people of this country are counting on us to deliver real relief. That means more jobs, faster economic growth, bigger paychecks, and a tax cut for Americans from all walks of life. These opportunities only come around once in a generation, and now it is time for us to seize this moment.”

Senate Majority Leader Mitch McConnell, R-Ky., called the Senate's passage of its tax bill a "great day for the country." He also defended pushing it through during the early hours of Saturday, after giving Democrats just hours to read through the changes before the vote.

"This was done through the regular order," McConnell said. "The Democrats had plenty of notice. Chairman Hatch can attest to all the multiple hearings, markups, open amendment process. Everyone had plenty of opportunity to see the measure."

Democratic National Committee chair Tom Perez slammed the bill as a "tax scam."

"This tax scam is an absolute betrayal of America’s working families," Perez said in a statement following the vote. "While Senate Republicans allowed virtually no debate or time to even read the hundreds of pages of hastily-drafted, handwritten bill text, they did manage to add dozens of new giveaways to special interest lobbyists."

Perez also said the bill disproportionately benefits the wealthy. "Republicans are unilaterally taking billions of dollars away from the middle class and handing it over to their billionaire donors and wealthy corporations while destroying the future of our economy," he said. "This is the price of Republican leadership: a tax plan built on lies and written for the rich, by the rich."

Sen. Elizabeth Warren, D-Mass., echoed Perez's sentiments, tweeting, "Tonight the @SenateGOP gave a giant tax break to the rich & left everyone else holding the bag ... This Congress doesn’t work for working families. It works for corporate lobbyists & campaign donors in backroom deals & 1:30 AM votes."

There were some fireworks just before the vote: Senate Finance Committee ranking member Ron Wyden, D-Ore., ridiculed the late-night, eleventh-hour vote, saying, "What's happening tonight is the worst of the United State Senate.

"This vote will not be forgotten," he continued, as senators in the chamber shouted for order as Wyden had gone over his time.

McConnell had told reporters Friday they had the votes to pass the legislation.

Just after noon Friday, Sen. Jeff Flake, R-Ariz., announced his support of the bill in a statement, officially giving it enough votes to pass.

“For nearly two decades I have advocated for a lower corporate tax rate that will enable U.S. business to compete globally and reforms that will deliver a fairer, simpler tax code," Flake said.

He added, "During the debate over the current bill, I’ve focused on two specific objectives. The first was to eliminate the $85 billion expensing budget gimmick in the bill. The second was to obtain a firm commitment from the Senate Leadership and the administration to work with me on a growth-oriented legislative solution to enact fair and permanent protections for DACA recipients.

"Having secured both of those objectives, I am pleased to announce I will vote in support the tax reform bill," he concluded.

Flake was one of three Senate Republicans whose votes were still up in the air Friday morning. Sens. Bob Corker, R-Tenn., and Susan Collins, R-Maine, were the other two holdouts. In the end, though, only Corker opposed the bill.

ABC News' Katherine Faulder contributed to this report.