"Look, in an ideal world, I think the deal is distasteful enough to say no to it," Hayden, who ran the CIA and National Security Agency for President George W. Bush, told CNN in an interview. "But I also realize that to pick up the pieces from that would require really powerful American engagement, and I have no confidence that's going to happen."
Hayden's doubt that the Obama administration would be able to persuade the P5+1 nations that negotiated the deal with Iran -- the United States, UK, Russia, China, France and Germany -- to restart negotiations with Tehran if Congress rejects the deal, led him to think the deal might be worth salvaging -- but only if there is bipartisan consensus to beef it up so Iran knows that the United States will insist it abide by the deal.
"Look, I'm really troubled by the deal. I'm not a fan. But I know how the American political system works," Hayden said about his compromise proposal. "When you actually pass something that the President feels like he needs to sign in return for getting a yes, he also gets some conditionality that the other political branch has insisted on."
Hayden argued that when Congress votes on the issue next month, it could add an authorization for use of military force, clearing the way for swift military action against Iran if that country moves to rekindle its military nuclear program.
Congress could add language to supply Israel, which is fearful the deal won't prevent Iran from building nuclear weapons, fresh armaments such as bunker buster bombs that could penetrate Iran's underground nuclear facilities.
Hayden said lawmakers also should consider lifting restrictions on exporting American oil in order to "meter the windfall the Iranians might get from this deal in terms of their own oil sales."
The deal provides Iran relief from punishing economic sanctions in return for curbs on its nuclear program. Republicans are expected to reject the deal en masse, but President Barack Obama has promised to veto their resolution. Republicans need 13 Senate Democrats and 44 House Democrats to join them to override the veto, but so far they haven't attracted that level of bipartisan support.
Top aides to lawmakers in both parties said they were not aware of Hayden's proposal until he first mentioned it Wednesday morning during an interview on MSNBC. They said it was too early to know how much support there would be to try to add the provisions, but said it is possible to amend the resolution Congress would consider.
One aide to a lawmaker who opposes the deal was doubtful Congress would want to approve a preauthorization of use of force.
Hayden acknowledged his proposal was still in the early planning stages.
"If I were at a National Security Council meeting, people would be yelling at me for not having specifics," he quipped. But he added that he thought his ideas might help bridge the partisan gap on the issue and get support from the political center.
A bipartisan agreement, he said, could provide future presidents the tools to keep Iran in line.
Because the White House is not treating the deal as a treaty, it wouldn't be legally binding in perpetuity even if the administration prevents Congress from torpedoing it. Several Republican presidential candidates have threatened to retract the agreement should they win the race.
"There is some virtue in a superpower having some continuity in its foreign policy," said Hayden, who is advising informally former Florida Gov. Jeb Bush's presidential campaign.