For Mrs. Clinton, the former secretary of state now running for president, the challenge is to walk a careful line between claiming credit for a much-criticized deal and positioning herself as tougher than her former boss. In a speech set for Wednesday, aides said, she will go beyond Mr. Obama by vowing to make it official policy to take military action if Iran races for the capacity to build a bomb, not just keep the option on the table, as he would.

Both are selectively presenting the history of the Iran issue. Mr. Cheney left out the fact that Iran went from a few hundred centrifuges spinning early in the Bush years to more than 5,000 when the two of them left office — a total the Obama deal would return Iran to. Nor did Mr. Cheney mention that the Bush administration ignored a diplomatic offer that would have limited Iran to just a few hundred centrifuges in a pilot plant.

Mrs. Clinton has her own spin on history. In the speech set for Wednesday, she will argue that she was a central player in escalating pressure on Iran through sanctions far tougher than anything the Bush administration put in place. Those included drastically limiting the country’s ability to sell oil and access international financing. She plans no reference to the other form of pressure: American and Israeli sabotage of the Iranian nuclear complex, a covert program that began under Mr. Bush and Mr. Cheney.

On probably just one thing do Mrs. Clinton and Mr. Cheney agree. “For every member of Congress, no matter how many years they serve or how many votes they cast, this will be a vote that will be remembered,” Mr. Cheney said at the American Enterprise Institute. “So much is in the balance for our own security and that of our allies.”

The back-to-back Cheney and Clinton speeches came as Congress returned to town to take up a resolution rejecting the agreement. While Mr. Obama had already secured enough votes to sustain a veto, four more Senate Democrats announced their support for the deal on Tuesday, and one came out against it.