Should the Senate go nuclear on the Iran deal?

Interesting poll results on the public's view of the Iran deal.  If you're white, black, hispanic, young, old, male, or female, the chances are you think it will make the world less safe.  The only demographic that slips over the 50-yard line toward support is Democrats.

Jim Geraghty threw out the idea last week that the Senate should defeat the deal on a majority vote.  Allahpundit picks it up and runs with it:

The question is, what do you do once the filibuster’s been nuked? If the GOP decides to pass a resolution declaring the Iran deal a treaty that requires two-thirds of the Senate to approve it, Obama will veto that resolution. That shouldn’t matter — since when is Article II contingent upon the president’s assent? — but you’re looking at a court battle at least, and the public will be bewildered after weeks of “does Obama have the Senate votes to protect his Iran deal?” headlines suddenly switch to “GOP changes rules on voting to block Iran deal.” They should have pounded the table about the treaty requirements from the beginning. Since they didn’t, though, maybe Geraghty’s plan could operate as a compromise solution, one that wouldn’t stop the deal but might embarrass Obama. If they nuked the filibuster, they’d at least get their resolution of disapproval to Obama’s desk, something Democrats are nervous about right now because of the message of no confidence it would send internationally in Obama generally and the Iran deal specifically. Iran may lose confidence that the deal will survive and look to back out. At a bare minimum, forcing a veto would be a political humiliation and a way for Republicans to wash their hands publicly of the outcome of this charade once it’s implemented. It’s a way to lay the whole thing in Obama’s lap. Having squandered all of their leverage, it’s probably the best play Republicans have left.

I'm trying to apply Cassandra's test to this approach: do we really want to sink to the level of some tactics just because we face them? Cassandra would make an excellent appellate judge, by the way: scrupulously fair, able to think through complicated ramifications, and determined to find rules that will serve equally well no matter whom they are applied to.  I don't want to see the filibuster undermined; on the other hand, it's been undermined, and I'll like to keep some balance in where it still applies.