Washington (CNN) -- In a bid to ratify the new nuclear missile agreement with Russia during the lame-duck session of Congress, the Obama administration is offering to spend $4 billion more over five years for nuclear weapons modernization.
Some Republican senators, led by Sen. John Kyl, R-Arizona, had questioned whether the Obama administration will provide enough money for modernization of the nuclear force remaining after the proposed START treaty cuts the number of deployed warheads to 1,550. The Obama administration already has proposed spending more than $80 billion to modernize the U.S. nuclear weapons complex over the next decade.
Kyl wanted an additional $4 billion. A senior administration official confirmed to CNN that the Obama administration is prepared to meet his demand.
The source, who spoke on background because of the sensitivity of negotiations, tells CNN that three administration officials flew to Arizona to brief Kyl on the deal. They also briefed congressional staff members, the source says.
President Barack Obama said Sunday he feels "reasonably good about our prospects," in comments to reporters on board Air Force One as it flew back to Washington from his overseas trip.
"We've been in a series of conversations with Senator Kyl, whose top priority is making sure that the nuclear arsenal that we do have is modernized. I share that goal," Obama said. "I think when we look at how important Russian cooperation has been on issues like Iran sanctions, on issues like transit into Afghanistan for our equipment for our troops, my hope and expectation is that, given this is a good treaty, given it has the support of previous Republican senior government officials, that we should be able to get it done."
However, the highest-ranking Republican on the Senate Armed Services Committee expressed doubts the new treaty will be passed by the lame-duck Congress.
"I don't know if that's possible or not, because there's going to be a desire, understandable desire on the part of Republicans, to do basically nothing except tax cuts and keep the government in action and obviously important," said Sen. John McCain, R-Arizona, in remarks to the the Foreign Policy Institute on Monday.
Meanwhile, two top Obama administration officials are warning "time is running out for this Congress" to ratify the new START treaty, which would cut the number of deployed nuclear weapons held by the United States and Russia by nearly one-third.
Secretary of State Hillary Clinton and Defense Secretary Robert Gates, in a joint editorial in the Washington Post, urged senators to act quickly on the agreement. Quoting President Ronald Reagan's maxim, "trust, but verify," Clinton and Gates say that since the old START Treaty expired last December "we have relied on trust alone."
"Until a new treaty comes into force, our inspectors will not have access to Russian missile silos and the world's two largest nuclear arsenals will lack the stability that comes with a rigorous inspection regime," the editorial said.
The new agreement with Russia, they say, will put in place an "effective verification regime to track each side's progress in reducing its arsenal to 1,550 strategic warheads. We will be able to count the number of deployed strategic weapons more accurately, because we will exchange more data on weapons and their movement than in the past. We will also conduct 18 short-notice inspections of Russian nuclear forces each year, including checking warheads on individual missiles."
Clinton and Gates also took issue with criticism from other Senate Republicans who argue that the agreement would limit proposed U.S. missile defense. In their joint editorial, they say the treaty "will not limit our ability to develop and deploy the most effective missile defenses to protect America's forces and territory, and to enhance the security of our allies and partners. This administration is committed to sustaining and improving our missile defense capabilities and has proposed spending nearly $10 billion in fiscal 2011 to do so."
McCain said he has two problems with the new treaty. "One is the whole issue of the modernization of our nuclear inventory. If we're going to reduce the inventory dramatically then we have to make sure that it's modernized and capable," McCain said.
The other aspect, he said, is "the whole issue of missile defense. I was very concerned about the signing segment that Russians made ... They stated any change in missile defense in Europe would be grounds for them to remove themselves from the treaty."
But McCain said those issues can be resolved. "I think that we can work that out, I really do."
He criticized those who claim passage of START would encourage other countries to expand their nuclear programs. "Anybody that alleges that a START treaty is going to effect the behavior of Iran or any other rogue nation and their desire to acquire nuclear weapons, that's just damned foolishness," McCain said.
CNN's Larry Shaughnessy contributed to this report.
