Democrats, meanwhile, were split, with some, like Senate Judiciary Committee Chairman Patrick LeahyPatrick LeahyThe Hill's 12:30 Report The Hill's 12:30 Report Passing US-Canada preclearance would improve security and economy 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 UdallGardner's chief of staff tapped for Senate GOP campaign director The untold stories of the 2016 battle for the Senate Colorado GOP Senate race to unseat Dem incumbent is wide open 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.