Looking at all available info about assimilation of cultures, I wonder if the Borg's first move would be to open up Transwarp conduits around Earth, to allow a more cubes into the area to facilitate assimlation.
If this happens, then there would be almost no resistance; they would transport drones to every inhabited zone, assimlate as many people as possible, then send those new drones out to assimilate more. I think the last free person on earth might last maybe a week, month tops in that scenerio. Of course, I'm using the Romero movies as a template.
If something like that doesnt happen, like they use only the cube and the Borged Enterprise, then I would assume things would take much longer. SF members are quite good at using their heads, and they might find ways to hide, at least until they could strike a blow. Could take a year, but remember, any losses by a resistance will either be lost (killed or destroyed), or converted to Borg assets.
After Earth falls (although they might not wait, they could start sending drones out to take the rest of the FED), they will begin converting all vessels and orbital habitats to borg designs, and taking over Luna and Mars colonies.
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"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth