Light aircraft pilot reported running off the end of the runway after rejecting the takeoff because of slower than normal acceleration; probably due to high density altitude.

Narrative

This event was an aborted takeoff around XAam on Day 0 from RWY 36R at NEW Lakefront Airport in New Orleans. Rwy 36R is 3697 ft long.Winds were checked immediately before engine start; and ATIS Oscar reported (if I remember correctly) about 110@4; which would have been a negligible headwind.After runup; when cleared for takeoff; Tower advised winds were around 160@ 4 or 6. I'm not sure of the exact winds. This would have been a small tailwind. I accepted the takeoff clearance for runway 36R. My mistake number one. I could have either declined the clearance or requested take off from the longer 6879 ft runway 36L or 18R. The next issue was density altitude. Takeoff was scheduled for 8am. Weather had first been checked about an hour before; and temperature was about 84F. While KNEW ASOS does state Density Altitude; ATIS does not. My mistake number two is that I did not call ASOS to verify Density Altitude; which I believe was about 1800 ft.During the takeoff roll; the airplane seemed to accelerate much more slowly than normal. At the runway midpoint intersection; airspeed showed under 45 kts. Rotation speed is 66 kts. I decided to abort the takeoff. Mistake number three is that I waited too long to make that decision and came to a stop in the grass about 30 ft beyond the end of the runway.I taxied back to the runup area; and the Tower told me to wait for the fire truck; which I did. We inspected the airplane; and I saw no damage. Engine run up was normal. I advised Tower that I was ready to takeoff; and Tower offered the longer runway; which sounded like a wonderful idea. Took off from rwy 18R and had an uneventful flight to ZZZ; landed; and then flew back home to NEW.I believe the airplane's lackluster performance was an effect of the higher than normal density altitude. Using the longer 6879 ft runway would have been such an easy solution.