Former Federal Reserve Chairman Alan Greenspan said Thursday that President George W. Bush's tax cuts should be allowed to expire because of the ballooning budget deficit. 

As Fed chairman during Bush's presidency, Greenspan oversaw the nation's monetary policy and endorsed the cuts before they were enacted in the early 2000s.

"I think they should follow the law and let them lapse. … Taxes go up," he told Bloomberg television in an interview to air Friday. "The problem is, unless we start to come to grips with this long-term outlook we're going to have major problems. I think we misunderstand the momentum of this deficit going forward."

Members of Congress are debating whether or not to let the cuts expire, or to extend them before they terminate at the end of the year. 

Some Democrats have argued for extending some of the cuts, such as those for households earning less than $250,000 per year. Republicans, for the most part, want the cuts kept in whole. 

Other Democrats have said the cuts should be allowed to expire to shore up the Treasury's coffers as a solution to stem the $1 trillion budget deficit. 

President Obama has promised not to raise taxes on households earning less than $250,000, placing pressure on Democrats on tax votes.