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Of the specific missile-defense language, Mr. Kimball said, “It has been clear from the get-go that the operative language in the New START treaty only affects offensive systems and it does not affect planned missile defense systems.”

He added: “This language is clarifying that fact. It is addressing a concern, albeit a silly one, that the Bilateral Consultative Commission might somehow reinterpret the treaty. Any changes to the treaty need to be approved by the Senate.”

On the other major issue for Republicans — the commitment to modernize the U.S. nuclear arsenal — the Obama administration has committed $624 million for the current fiscal year and plans on making that $1.6 billion for the next fiscal year.

Senate Republicans and the heads of the U.S. nuclear labs have expressed worries that most of the funding for the modernization comes more than four years from now and thus may not be enough to fix problems with the aging arsenal.

The draft resolution from Mr. Lugar states that if there is not enough money for nuclear-infrastructure modernization, the president must submit a report to Congress to determine whether “in the changed circumstances brought about the resource shortfall, it remains in the national interest of the United States to remain a Party to the New START Treaty.”

Thomas D’Agostino, head of the National Nuclear Security Administration, the Department of Energy agency that oversees the U.S. nuclear labs, said in an interview Monday that he has received high-level White House support for plans to modernize the U.S. nuclear-weapons infrastructure.

Sen. Jon Kyl, Arizona Republican and a key figure supporting the nuclear-modernization issue, told reporters last month that he may be seeking more money and an independent revenue stream for the modernization project. He did not, however, commit to specific increases.

Mr. D’Agostino said that the four main projects he supported for modernization included a new uranium-processing facility; a chemistry and metallurgy research facility; upgrades to the B61 nuclear gravity bomb program; and a new “life-extension” program for the W78 and W88 nuclear warhead.

“It’s difficult for anyone to say how much those projects are going to cost now. These are the projects that need to be baselined,” he said when asked about Mr. Kyl’s concerns about funding for nuclear-arms upgrades.

“It may end up being the projects are at the upper end of the ranges we previously had estimated. That is no problem because the administration says they are going to support these projects.”

Mr. D’Agostino said that in the next two months he was going to receive new audits on these projects for their costs and begin the process of determining “how much it will cost, and what you need to build, and how long it takes to build.”

For now, Republicans are still waiting to follow the leads of Mr. Kyl and Mr. Lugar. Don Stewart, a spokesman for Senate Minority Leader Mitch McConnell, Kentucky Republican, said, “The minority leader has said Sen. Lugar and Sen. Kyl are the leaders on this. If they both support the treaty, it makes it a lot easier to proceed with it, and if they don’t, then it doesn’t.”