I can't help but think that if the Senate voted affirmatively that climate change was real, then everyone would applaud them and the article would not have been posted. Like a lot of things, what seems to work and not work is very situational, based on whose ox is getting gored.
That said, while it should not be particularly relative what a legislative body thinks of a scientific issue -- after all, scientists aren't voting on whether or not the Senate is deeply, hideously, irrevocably corrupt, stupid, and incompetent -- a political stunt like that sets the tone for a lot of people who are just looking to have their particular bias confirmed -- "Oh, hey, look what the Senate said...normally while I hate government, I'll put that aside for a second and be glad they agree with me! Murka, hell YEAH!"
Overall, the fact that this vote took place shows just how badly science, along with everything else in this country, has become politicized. The political debate should be a non-starter, and efforts to reduce carbon emissions should simply be a policy like not dumping barrels of plutonium into the sea or letting rivers catch on fire.