I'm attempting to use tapcon 1/4in by 2.75in concrete screws to affix something to a wall of poured concrete, but it's only going about 3/5 of the way in before refusing to go any further. I used the recommended tapcon drill bit size so I don't think that's the issue, and I've also air blasted all the dust out. What else could it be? Do I just need a more powerful drill? A smaller size screw?
That's far too long a screw for that application. 2-3/4" screws are designed for mounting 2x4 lumber, for example, which would leave just 1-1/4" of penetration or so.
Concrete screws, especially thinner ones like that, should only engage the concrete maybe an inch or a bit more. If you try running that in with a stronger drill it'll almost certainly snap.
Try the 1-1/4" screws, and be aware that running them in more than once usually results in the threaded concrete failing due to the grinding effect of insertion. They should be a once-and-done install. Move to a new hole if that one doesn't seem to hold with a shorter screw, or use some epoxy to rebuild the bond.