WASHINGTON, Jan 11 (Reuters) - U.S. Senate Majority Leader Harry Reid said on Thursday he expects to have the votes, with the support of some Republicans, to pass a resolution opposing President George W. Bush's proposal to increase troops in Iraq. Though such a resolution is nonbinding and merely reflects opposition in the Senate, Reid said, "I think that (bipartisan passage) will be the beginning of the end of the war in Iraq." Democrats, who control the Senate with 51 of 100 seats, would need 60 votes to clear a possible Republican procedural roadblock. Reid said he plans to introduce the measure next week. "We expect to have 60" votes, Reid said, noting that at least a dozen Senate Republicans have come out against the increase of 21,500 troops proposed by Bush. "We have a lot of support from Republicans," he added. Senate Minority Leader Mitch McConnell, a Kentucky Republican, refused to offer a prediction on the outcome of the vote.