、。
All right, let's have a contest of endurance.
Literal
Well-then, endurance-contest [obj-を] do-[let's-しよう].
さあ is an attention-getting interjection 'come on / well then,' used to urge action. 根比べ (literally 'root-comparison') is a compact native compound for 'contest of endurance / battle of wills / seeing who gives up first,' where 根 'root' metaphorically stands for 'tenacity / stamina.' The volitional しよう 'let's do' gives an active proposal.