So I am having tire floor pump issues.

I bought a Topeak Joe Blow, but couldn't pump my thin bike tires. I asked a guy at a LBS and he said I needed a pump with a smaller air cylinder.

So, I bought a Specialized pump at another LBS today. This one has a narrower pump cylinder, and is much easier to pump. However - my tires are now rock hard (as they should be), but the pump says that I am at 60 PSI. The recommended PSI on the tire says 117. I even check with the Joe Blow, and that gauge also says that the tires are at 60 PSI.

So now I am stumped. I got a pump that worked, and my tires feel right, but the dial says that I am at half the PSI that I should be. Should I keep pumping until I am in that 110-115 range? Will I blow out my tire? Am I neglecting to notice something else?

Has anyone else had pump/tire issues?