There would be the possibility, not the certainty, of some off flavors.
I started reading "The Joy of HomeBrewing", and I am generally a believer that even sub-optimal conditions can produce good beer.
If you can't get lagering type temperatures try finding a recipe that uses WYEAST California Lager or WL San Francisco Lager yeast. Both work in the high 60's, but do benefit from a mid 50 range fermentation.