House lawmakers are expected to tackle a spending bill after leadership pushed a vote originally expected on Wednesday.
But the Tennessee Republican said there's been discussion of the incident.
Sen. Ben Cardin warned the amendment was a "poison pill" for the legislation.
The provision would require certification that Iran supports Israel's right to exist.
Senators are discussing which amendments to consider on the bill.
Republicans said they are "perplexed" by the administration’s threat assessment.
The Democratic leader used Barrasso as an example of Republicans being "relentless" on Obamacare.
McConnell pledges to take up Obama's trade push after the Iran bill.
The majority leader said it was "appropriate" given Tuesday's events that senators were debating Iran legislation.