Democrats, meanwhile, were split, with some, like Senate Judiciary Committee Chairman Patrick LeahyPatrick LeahyDem senator asks for 'top to bottom' review of Syria policy A guide to the committees: Senate Verizon angling to lower price of Yahoo purchase: report MORE (Vt.) and Sen. Kent Conrad (N.D.) arguing that the Congress should not tamper with the Constitution but balance the budget annually on its own volition. Other senators like Sen. Mark UdallMark UdallElection autopsy: Latinos favored Clinton more than exit polls showed Live coverage: Tillerson's hearing for State The rise and possible fall of the ‘Card’ in politics MORE (D-Colo.), however, expressed support for a limited version of the amendment expressed in S.J.Res 24.

That Democratic version would prevent Congress from lowering taxes on millionaires and also exempt the Social Security trust funds from the amendment's accounting. 

The Senate spent hours in a break and in quorum calls on Tuesday afternoon.