You are equating things that are several orders of magnitude different in scale. Ie, this is a much bigger project than a translantic cable - you are off by perhaps 3 order of magnitude. And there has never been a time since wires were invented (much less decades after they were invented) that they could only be produced in microscopic quantities and for thousands of dollars a gram. So production of carbon nanotubes will have to improve by, oh, I dunno, ten orders of magnitude in both cost and scale.
So I would say, as a rough guess, that a carbon nanotube space elevator would be around 10^23 times more difficult to do than a translantic cable. It puts it on similar footing with things like anti-matter propulsion.
In order to start with the assumption that 'anything is possible', like you said you do, you are assuming that we will discover new technology with the absence of any scientific basis for the assumption. Such assumptions are unscientific and wrong. Fred said "even if". I'm not completely certain what he meant, but my position, if I were willing to let the first "impossible" go, would be "even if" we get past the first 'impossible', there is another one right behind it. But I'm not willing to let the first ''impossible' go.
BTW, I'm pretty sure you once suggested that it is best to start out with no assumptions. The 'anything is possible' assumption is the crank assumption that makes this a cranky subject.