Democrats, meanwhile, were split, with some, like Senate Judiciary Committee Chairman Patrick LeahyPatrick LeahyGoing national with automatic voter registration Republicans slam Trump’s new policy toward Cuba Trump draws a harder line on Cuba 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 UdallDemocratic primary could upend bid for Colorado seat Picking 2018 candidates pits McConnell vs. GOP groups Gorsuch's critics, running out of arguments, falsely scream 'sexist' 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.