"The Iranian behavior and rhetoric have been so provocative, that there's a decent chance Congress could kill this thing," Valliere said.
Read MoreIran diplomats: Nuclear deal likely Monday into Tuesday: Sources
While President Barack Obama would override any congressional motion of disapproval, Valliere said Congress would attempt to overturn the veto. "That's going to be a close call," he said.
Analysts said the details of the deal will be important. The agreement was expected to impose strict verifiable limits on Iran's nuclear program to prevent it from advancing to weapons development.
Dan Clifton, head of policy research at Strategas, agrees Congress will attempt to roadblock the deal but he expects it ultimately to be approved.
Congress has 60 days to review the agreement but in several weeks it will go on recess until September, delaying the process. That could also potentially give opponents more time to galvanize their case, Clifton said.
Valliere said in the Senate, the one to watch is Sen. Chuck Schumer, D-N.Y., who he described as "lukewarm at best." Senate Majority Leader Mitch McConnell over the weekend described the deal as a "hard sell."
"You need a two-third supermajority to override the president's veto," Clifton said. He said absent a change in the review process, "it would be difficult to get House Democrats to embarrass the president on the world stage."
One reported sticking point was Iran's efforts to have a conventional weapons embargo lifted.
Iran has said it could bring 1 million barrels a day back to the market, but analysts say that would be difficult without foreign investment.
Analysts vary on how much Iran could quickly add to the world market. Some say it would take several months to restore 300,000 barrels a day, and that it could then increase its exports to 500,000 barrels within six months.
The prospect of more Iranian crude on the market has helped drive oil prices lower. West Texas Intermediate settled down 1 percent Monday at $52.20 per barrel.
Citigroup said in a research note that it believes that export sanctions are unlikely to be lifted for six months after a signed agreement.
"That's because it is likely to take a good six months post agreement for the IAEA to confirm the reduction in centrifuges in the country, the elimination of interconnections between centrifuges, the export of enriched uranium above allowable levels and the establishment of a working and workable monitoring system. Before that happens, many political obstacles remain," Citi analysts wrote.
John Kilduff of Again Capital believes some additional Iranian oil could begin to come onto the market even before final approvals.