CNN's Jake Tapper, anchor and chief Washington correspondent, and CNN's Dana Bash, chief political correspondent, moderated the debate, which was in Washington.
Cruz began by defending the Republican's tax plan, and called on Congress to lower taxes overall.
"Bernie and the Democrats want every one of you watching today to pay more taxes, and Republicans want to lower the taxes for each and every person watching this debate," Cruz said.
He later said the objective of tax reform should be cutting everybody's taxes.
Sanders said that although he supports "a tax cut for the middle class and working families," he does not support tax breaks for the most wealthy individuals.
"What this entire proposal is about is to give tax breaks to people who don't need it," Sanders said during the debate, adding it would be at the expense of other programs that working families depend on.
According to the tax reform "framework" that Republicans released last month, the plan would lower the corporate rate to 20%, reduce the number of income tax brackets from seven to three, double the standard deduction, increase the child tax credit and repeal the estate tax.
Many key details are still missing and Republicans have yet to release the full bill, waiting on the Senate to first pass a budget resolution. House Ways and Means Chairman Kevin Brady suggested last week that the legislative process in the House would begin soon after the budget was passed.
So far Republicans have agreed to a tax cut that would cost $1.5 trillion over the next 10 years. While Trump officials and Republican leaders argue that economic growth will pay for the cuts, Sen. Bob Corker, R-Tennessee, has been adamant that he won't vote for any tax reform bill that will add to the deficit.
Others, like Cruz, want an even deeper tax cut, believing it will generate even more economic growth. "I think this should be an unapologetic tax cut," he said last week on CNBC.
The Senate is set to vote on a budget resolution later this week that will make it possible for Republicans to use reconciliation on tax reform, a process that allows them to pass it with only a simple majority of 51 votes, rather than the usual 60 needed to overcome a filibuster.
That means Republicans, who hold a 52-48 majority in the Senate, could pass tax reform without any Democratic votes and still afford to lose two from their own party, with a tie-breaking vote from Vice President Mike Pence. Reconciliation can only be used once each fiscal year, and even though Republicans used it to help pass a health care bill, they still couldn't rally enough votes within their own party to get to a majority.
This time Republicans are hoping to get some Democrats on board in case they once again fall short. President Donald Trump has taken his tax reform message on the road to states that he won last year and have vulnerable Democratic senators up for reelection in 2018. It's an attempt to ramp up pressure on senators like Heidi Heitkamp of North Dakota, Joe Manchin of West Virginia and Claire McCaskill of Missouri.
Those three senators also dined with Ivanka Trump and Jared Kushner
in a bipartisan dinner in Washington Monday night, where the group discussed tax reform, more specifically the President's push to increase the child tax credit, which has broad support across party lines.
Don't count Sanders, however, in the mix of potential senators who might side with Republicans. The 2016 presidential candidate described Trump's tax plan as "morally repugnant and bad economic policy" in a statement last month, saying it disproportionately benefits the wealthy over the middle class.
The goal is to pass the bill by the end of the year, and House Speaker Paul Ryan threatened last week to keep members in session on Christmas
to get it done. While Senate Majority Leader Mitch McConnell and Trump also say they want to finish by year's end, both men softened expectations in a news conference Tuesday, pointing to previous administrations that didn't finish major legislative tasks quickly.
"The goal is to get it done this calendar year," McConnell said. "But it is important to remember that Obama signed Obamacare in March of year two. Obama signed Dodd-Frank in July of year two."
The debate will air on CNN, CNN en Español, CNN International, and will be carried by CNN's SiriusXM Channel 116 and the Westwood One Radio Network.
In addition to the TV airings, the debate will also stream live for subscribers via CNNgo (at CNN.com/go and via CNNgo apps for Apple TV, Roku, Amazon Fire, Samsung Smart TV and Android TV) and on the CNN mobile apps for iOS and Android. The debate will also be available Thursday via on demand via cable/satellite systems, CNNgo platforms and CNN mobile apps.