No, you don't have to use a circular needle, it'll just make it easier to have so many stitches on your needles.
How long are your straight needles? I think the longest they are generally made is 14". If you are having trouble craming your 84 stitches onto 14" needles, the next best step might be a circular needle. You might be able to find longer custom made straights, but with all those stitches on them they will be awkward to work with and probably heavy, too. Using a circular needle will be much easier to get all 84 stitchs on and more evenly distributed so it won't be so heavy, either.
Blankets can also be knit in sections and seamed together, if all you have to use is the 14" straights.