The next two weeks will be key, at least in the Senate, where lawmakers are eyeing multiple avenues to object to the administration's recent actions affecting the Persian Gulf.
As soon as Tuesday, senators could manoeuvre to block up to 22 arms deals, most of them benefiting Saudi Arabia and the United Arab Emirates, that the administration last month invoked emergency authority to complete, over congressional objections. It is unlikely, however, that all 22 disapproval resolutions will receive a vote on the floor - not least because another potential vehicle for thwarting the move is due for consideration.
Senate leaders plan to tackle their chamber's version of the annual defense bill before the end of June. The $750 billion authorization bill is one of the few must-pass measures Congress considers in a given year - and is prize territory for opponents of Trump's arms sales and Iran policy to attach measures seeking to constrain him.
Democratic senators are planning amendments to limit the president's emergency authority when it comes to concluding arms sales. In theory, the move has at least some Republican support - including from Graham. They also are pushing for an amendment prohibiting federal funds from being used for military operations against Iran unless the administration has first obtained express authorization from Congress to conduct such hostilities.
Lawmakers have struggled for years over how to prevent the commander in chief from claiming sweeping powers to engage in the Middle East militarily, despite calls from Capitol Hill to revisit the 2001 and 2002 authorisations for the use of military force. The AUMFs were initially approved for operations against al-Qaeda and Taliban affiliates, and in Iraq.
The House's defense appropriations bill would end the 2001 AUMF. But in both chambers, Democrats also want to demand expressly that the administration consult Congress before confronting Iran.
In the Senate, Republican leaders need to permit votes on amendments to the defense bill. That means the House, where Democrats are in charge, could prove a more fruitful arena.
Earlier this week, House Armed Services Committee Chairman Adam Smith, D-Wash., promised members a full House vote to prevent "an unconstitutional war in Iran" - even if Democrats go it alone. House leaders also are planning a measure that would restrain the president's emergency powers on arms sales.
Should either chamber work those amendments into the defense bill, that will be part of the negotiations between the House and Senate over the final product.
But in the past, negotiations have taken months - and time is potentially of the essence.
Unless Congress acts soon, at least some of the weapons contracts will probably be fulfilled. And while Trump has said he is "in no rush" to decide whether he will respond to the oil tanker attacks, any move he makes could dramatically change the Iran debate on Capitol Hill.