The difference in the climate today is that one party was essentially saying no to anything Obama might do. Even if they privately agreed or could find some ways to agree with him, they knew that if they so much as smiled in his direction they'd get primaried and kicked out. That climate poisons the relationship between the branches, and gets you to non-standard processes which we can all agree are sub-optimal.
For a balance of powers system to work you need to actually have a working relationship between the branches. It's not going to work if one says, "NO!" then expects the other branch to take their toys and go home. In the real world, we all have to accept compromise toward our objectives, and if we don't we'll get disaster for all our objectives down the line.
Kind of a moot point IMO, given the current state of the GOP. Had Obama gone to Congress they probably would've reflexively voted it down anyway. The current GOP is willing to damage America's trustworthiness on the world stage and this is more proof to the point.
I don't know if most mainstream Republicans would've done something as drastic as this after the accord had been agreed to but Trump is basically the head of the party now so here we are.