Shortly after President Obama announced a nuclear deal with Iran on Tuesday — and long before the detailed text became available — verdicts began flowing in from lawmakers. Some were already vowing to “undo” the agreement, others gave tepid support, but nearly all ignored the reality: that while Obama’s achievement faces a tough sell on the Hill, even if lawmakers were to oppose his push, they have no real kill switch.

“I want to read the agreement in detail and fully understand it, but I begin from a place of deep skepticism,” said Senate Foreign Relations Committee Chairman Bob Corker, R-Tenn. “Relieving sanctions would make the Tehran regime flush with cash and could create a more dangerous threat to the United States and its allies.”

Corker has said throughout the negotiations that the administration “crossed red line after red line.” His committee has primary jurisdiction for reviewing the deal, under legislation he pushed through debate and brinksmanship to a 98-1 vote in May.

Sen. John McCain, R-Ariz., the chairman of the Armed Services Committee, said that while he’ll “thoroughly review” the details, “all signs point to this being a bad deal.”

On the other side of the aisle, Sen. Dianne Feinstein, D-Calif., ranking member of the Intelligence Committee, called the deal historic. “It offers a verifiable, diplomatic resolution to one of our most pressing national security challenges,” she said. “I believe it will stand the test of time.”

But other Democratic colleagues predicted that Iran would quickly test the limits of the agreement. Even as House Minority Leader Nancy Pelosi, D-Calif., praised the deal as “the product of years of tough, bold and clear-eyed leadership from President Obama,” she warned, “We have no illusions about the Iranian regime…All options remain on the table should Iran take any steps toward a nuclear weapon or deviate from the terms of this agreement.”

The partisan tone of the reactions is predictable; many lawmakers made up their minds long before the agreement was reached. “Whatever deal comes out this weekend, it’s going to be dangerous for the United States and dangerous for the world,” Sen. Tom Cotton, R-Ark. said on Sunday.

Some GOP presidential candidates have been promising for months to reverse the putative deal if they become president. The latest is Wisconsin Gov. Scott Walker, who announced his candidacy just hours before the diplomats concluded the agreement in Vienna. “We need to terminate the bad deal with Iran on the very first day in office,” Walker said.

But his four rivals for the Republican presidential nomination who are launching their campaigns from Congress know it’s not so simple. Missing from all the rhetoric is the inconvenient logistics: Obama’s announcement is only the beginning of a complex, interlocking series of steps to review and implement the agreement. And the review process set up by Corker’s legislation may favor the administration’s deal rather than efforts to block it.

Still, opponents predicted the deal might die in Congress. Sen. Marco Rubio, R-Fla., called the deal bad for national security and predicted that “a significant majority” would vote to disapprove. “Failure by the President to obtain congressional support will tell the Iranians and the world that this is Barack Obama's deal, not an agreement with lasting support from the United States,” Rubio said.

“It’s going to be a very hard sell, if it’s completed, in Congress,” Senate Majority Leader Mitch McConnell, R-Ky., said on “Fox News Sunday.”

But then there’s the math: Congress needs a two-thirds majority in both chambers to override the veto; Obama needs only the support of 34 senators to give the agreement safe passage.

After some paperwork, the deal will be submitted to Congress, beginning a 60-day period of public debate and congressional review. (The May law allows the House and Senate to seek an 12-day extension by sending a joint resolution to the president.) During that time, Congress can vote to approve or disapprove of the deal — or not act at all. If lawmakers vote no, and Obama makes good on his promise to veto such a decision, Congress will then have 10 days to try to override it.

Under that law, Obama is prevented from waiving or suspending congressionally imposed sanctions on Iran before Congress approves or disapproves (or ignores) a final agreement. But that doesn’t include other U.S. sanctions or those imposed by the United Nations, which Obama said will be lifted in phases as Iran takes steps to implement the deal. Sanctions on Iran’s access to arms and ballistic weapons will remain in place for five years and eight years respectively. Under details of the agreement released by the Obama administration, the deal’s stipulations would be adopted in a United Nations Security Council resolution that’s already being prepared.

Iran is expected to be granted billions in relief from the economic strictures — but, Obama reiterated, “If Iran violates the deal, all of these sanctions will snap back into place.” The “snap back” would restore sanctions in 65 days, according to diplomats involved in the negotiations.

Corker told reporters Monday night that Congress is unlikely to vote until September, at the earliest. Much of the 60-day period will be eaten up by Congress’s long summer recess, and, as is typical of this time of year, lawmakers are already scrambling to pass critical legislation, such as the dense authorization and appropriations bills, and warning about another shutdown in September.

Secretary of State John Kerry said Tuesday he doesn’t think lawmakers will vote down the deal.

“If Congress were to veto the deal, Congress – the United States of America would be in noncompliance with this agreement and contrary to all of the other countries in the world,” he said. Obama has vowed to veto any legislation that prevents the deal’s implementation.

If Republican senators do try to block the deal, they will likely woo Democratic Iran-hawks such as New York’s Chuck Schumer and New Jersey’s Bob Menendez. Both said Tuesday they wouldn’t be easily bought by intensive lobbying from either Republican colleagues or the administration.

“I intend to go through this agreement with a fine-tooth comb,” Schumer said. “Supporting or opposing this agreement is not a decision to be made lightly, and I plan to carefully study the agreement before making an informed decision.”