Democrats, meanwhile, were split, with some, like Senate Judiciary Committee Chairman Patrick LeahyPatrick LeahySessions: No plan to recuse from DOJ Trump probes VA leaving navy veterans adrift in sea of Agent Orange Senate confirms first nominees of Trump era 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 UdallLive coverage: Tillerson's hearing for State The rise and possible fall of the ‘Card’ in politics Gardner's chief of staff tapped for Senate GOP campaign director 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.