Without the background of a ongoing cold war with a rival superpower, could a Colossus be set in modern times?
It doesn't have to be a rival superpower. Just two computers linking and forming one massive, "all knowing" supercomputer would be enough to set things in motion. Especially with the way computer technology is today as compared with the 70s. The supercomputer could easily hack and enslave all the other computer systems in the world, thus taking control of very nuke regardless of country of origin.
You actually don't have to fundamentally change anything. The US is even more dependent on automated defense systems now than it was back in the 70s. With UAVs regularly in the news now, the idea that the US would construct an autonomous computer system to manage it all is not that far fetched.
You could even keep the Russians as the potential rival. The Cold War my officially be over the but the Russians are actually MORE paranoid now than they were at the height of the Cold War. They are freaking out about the US building an ABM system that does not work and that they could easily overwhelm. So its not beyond the realm of possibility that they might build a rival computer system if they even thought that the US might build one. Indeed you could even make it a three/four way race between the US, Russia, China and the EU.