ABC News’ Matthew Jaffe reports: Supporters of the START nuclear pact with Russia today sounded confident that the treaty will receive the two-thirds majority needed for Senate passage when it comes up for a final vote this week. “I believe we have the votes to pass this treaty,” said Senate Foreign Relations Committee chairman John Kerry at a brief press conference on Capitol Hill. Kerry and the panel’s ranking Republican Dick Lugar made similar comments yesterday on “This Week.” That confidence appeared warranted today as momentum seemed to be building for the treaty. After a closed Senate session to discuss classified information relating to the pact, Republican Scott Brown of Massachusetts told reporters that he would back the treaty. “I believe it’s something that’s important for our country and it’s a good move forward to deal with our national security issues,” Brown said. Sen. Bob Corker, R-TN, indicated that he would almost definitely vote for the treaty. “I’m in the same place I was the day I voted to pass it out of committee: the Ts are being crossed and the Is are being crossed. Something could change, but I don’t know what that would be,” said Corker. In addition to Lugar, Brown, and Corker, other GOP senators such as George Voinovich of Ohio and Olympia Snowe and Susan Collins of Maine have also said they will vote for the treaty. The GOP’s Judd Gregg of New Hampshire has said he is inclined to support it, while Sen. Thad Cochran of Mississippi also plans to vote for it, according to Democrat Chuck Schumer of New York. Cochran later told Roll Call that he is still evaluating the pact. If those eight senators back the treaty, that means the pact would only need one more Republican vote for ratification. That vote could come from a handful of GOP senators such as Johnny Isakson of Georgia, Lisa Murkowski of Alaska, Bob Bennett of Utah, or John McCain of Arizona. A procedural vote on ending debate on the treaty is set for Tuesday morning. The treaty will need 60 votes to make it past the procedural hurdle, but that appears to be a mere formality at this point. A final vote could then come later Tuesday or sometime on Wednesday. A spokesman for Democrat Ron Wyden of Oregon, who underwent prostate cancer surgery on Monday, said the senator would do whatever possible to cast his vote on Capitol Hill if his vote is needed. If all 100 senators vote, the treaty would need 67 votes for ratification. If 99 senators vote, it would need 66. Republican leaders Mitch McConnell of Kentucky and Jon Kyl of Arizona have both announced their opposition to the pact.