The 48v thing *could* be a problem, in my experience. A new cable definitely won't help that. I have a couple of C414 condenser mics that sound thin, small, and crappy when I try to run them (either or both, but especially both) using phantom power off of my bus-powered firewire interface. I have other condensers that are just fine with the power from the interface, and I'm not familiar with the requirements of
the blue bird.
*If* this is the problem (and I agree with the immediately prior posters that it's more likely related to placement or gain staging or something else), a sure-fire and inexpensive way to solve it is to get a dedicated inline phantom power supply that plugs into the wall and sits immediately behind the mic (um, and you will need to have a new cable, because you'll need two - one from the mic to the power supply, and one from the power supply to the Icicle or whatever else you're using). That's what I did for the C414s. Just a suggestion.
Definitely try the not-buying-anything approaches first. And if you have a cheap Chinese condenser mic (especially small diaphragm) and/or one that uses an electret biased capsule to try out with the Icicle, it's unlikely to have big power requirements, and so if it seems to work a lot better than the Bluebird, that may be an indicator that it's a phantom power problem.
Many nice preamps supply ample phantom power, too, but that alone isn't a good reason to get one - they cost a lot more, and a preamp alone won't replace the Icicle, since
the Icicle's also performing analog to digital conversion and interfacing with your computer. You'd be shelling out major dough either for a pretty nice interface or a combination of components before you were done going down that route.