To suck it up means to endure something painful or unpleasant, but the speaker in this context is considering not enduring it in order to avoid hearing what the other person has to say.
Context: "I'm stuck between the desire to run away quickly to memorial church, the nearest hallowed ground I can think of-or to not endure and not hear what he's going to say this time." Claim: "I'm torn between the desire to run-hightail it straight to memorial church, the nearest hallowed ground I can think of-or to suck it up and hear what he's going to say this time."
Considering the context, is the claim true, false, or unknown?