How faint can a positive be?
It really depends on if there is any color to the line. If it's just a grayish colorless line then it is more than likely just an evap line showing up. If there is a hint of color to the faint line, then it's probably a very early BFP. Are the test(s) you're using pink dye or blue dye? It's really hard to tell a faint BFP from an evap with blue dye tests.
This happened to me. I was 2 days past my longest LP and I got the faintest of lines. It was a pink dye, early test and both dh and I stared and stared trying to decide if we were seeing things. I got my period 2 days later. But the happy news is that I conceived dd the very next cycle. Nothing like a m/c to kick your body into gear!
Oh yes... take a picture next time!