The effect on the gulf stream from Climate change: unprecedented threats?

I watched a programme the other night called “how to survive armegeddon". It was a programme from the discovery channel if I remember correctly. It highlighted ways in which humanity faces extinction and the demise of our species, it didn't offer much hope as you can imagine. Anyway one of the ways they stated humanity could cease to be is from the apocalyptic effect on the gulf stream from climate change. It said that If we do nothing we agree that we are all going to die without trying to save ourselves, it said that rising sea levels, that threaten to flood all coastal regions around tue world, forcing millions inland in the next 80years, will effect tue warmth of the stream. It stayed that Europe will endure a cataclysmic 100 year winter that would kill millions of people as we endure temperatures of -25 many will freeze to death within months. The test of tue world would face drought and starvation. The programme effectively stated that the human race faces extinction within 100years if we do not stop, or halt the rapid change in the climate that threatens to engulf the worlds Coastal regions and put entire countries under water. The programme concluded that climate change and the effects on the gulf stream is the single biggest threat to our survival and If we do nothing, come 2050 the world will start changing for the worse. Is this correct? Would the gulf stream be effected this way?