"Expect high level, robust engagement with the Hill regarding the deal," a White House official said, if an agreement can be reached.  That sales pitch would come after what has already been a concerted effort to convince lawmakers from both parties in Congress to hold off on legislation that would give members a vote on any deal. President Barack Obama has vowed to veto such a bill.  Instead, the White House will want lawmakers to remain largely on the sidelines for the next several months as the U.S. and other world powers continue to work though the technical details of a final deal to constrain Iran's nuclear program. The deadline for that comprehensive agreement is set for the end of June.  RELATED: Iran's power rises, with or without deal  "We've been working very hard to keep Congress briefed and up to date on this. I believe if you count up our engagements with Congress on this issue they total in the hundreds," White House spokesman Eric Schultz said Monday.  By and large, Republican leaders are far from convinced the Obama administration will hammer out an effective agreement.  "When you begin to see all these leaks that probably came out of the White House in terms of what the Iranian deal was starting to shape up to be, there's a lot of concern in congress on a bipartisan basis," House Speaker John Boehner, R-Ohio said on CNN's "State of the Union" Sunday before traveling to Israel to meet with Prime Minister Benjamin Netanyahu. Boehner said the visit was planned months ago.  A top GOP aide complained while the White House has kept lawmakers abreast of the administration's progress in the nuclear talks, members of Congress hardly have a say in the matter.  "I don't think they're looking for input, and they certainly don't want us weighing in," the Republican spokesman said.  Adding to what could be a messy battle over the Iranian issue between the White House and GOP lawmakers are some hard feelings among Democratic officials that Republicans have politicized a sensitive diplomatic process. Exhibit A, Democrats say, was Boehner's decision to invite Netanyahu and the Israelis to lobby Congress against an agreement.  "The GOP made this a partisan issue. Democrats like Republicans would like to see the details. President Obama's insistence on sanctions got Iran to the table. Now, they have to work out the politics," a senior Democratic official said.  But members of Congress from the President's own party have questions for the administration. Last week, a handful of them sat down for dinner with Israel's ambassador to the U.S., Ron Dermer, who has led his country's lobbying efforts on Capitol Hill against a nuclear agreement with Iran.  RELATED: House Democrats to dine with Israeli ambassador  "No surprise to anybody that when you have dinner with Israel's ambassador to the United States Israel's ambassador is going to weigh in with his deep and grave concerns about a deal with Iran. I am very skeptical about any deal," said Rep. Steve Israel, D-New York.  Much of the coming White House sales pitch will depend on just what is actually accomplished in the nuclear talks in Switzerland. Negotiators are still haggling over the specifics of the framework agreement, while the technical details of a deal, or "annexes" as they are known in diplo-speak, won't come until late June. Just how much uncertainty is baked into the initial agreement could drive the debate on Capitol Hill.  Aaron David Miller, a Middle East Analyst with the Wilson Center sees two possibilities in the framework agreement. "A short outline with key provisions made public and more detailed, classified briefings to the Hill. Or, an actual six to eight page document that really does demonstrate considerable detail. Either way, they'll have to sell."  RELATED: Centrifuges and secret sites: Get up to speed on the Iran nuclear talks
With foreign ministers in Switzerland scrambling to cobble together a framework agreement to roll back Iran's nuclear program, the White House is readying the next phase of any deal -- selling it to the American public.