MORE: (No longer flippant) If Wolsey fell, the splash would swamp a few small boats like ours. There will be no new Chancellors while Wolsey lives. (1.380)
While Wolsey is still Cardinal, More can rest easy—it provides a barrier between him and the King. But, as we all know, old Wolsey bites the dust pretty early on in the play, which leaves More terrifiedof what might come next. Whatever it is, it's not going to be pretty.
STEWARD: So he's worried, sir…(CROMWELL is interested) Frightened…(CROMWELL takes out a coin but pauses suspiciously) Sir, he goes white when it's mentioned. (1.425)
The subject Cromwell and Matthew are discussing here, by the way, is the King's divorce. More has refused to talk to anyone about the matter since becoming Chancellor, and this interaction reveals the very simple reason behind his reluctance: fear. Good old fear. You might laugh, but you'd be quaking in your boots too if you were in this situation.
MORE: [...] Alice… (She turns) Set your mind at rest—this (Tapping himself) is not the stuff of which martyrs are made. (1.617)
In other words, More is saying that he's too much of a scaredy-cat to get himself into trouble. We're not so convinced. Although it is obvious that More is terrified of what could happen to him (and his family), it's equally obvious that he won't back down.
RICH: You wouldn't find him easy to frighten! (CROMWELL exits. He calls after him) You've mistaken your man this times! He doesn't know how to be frightened! (1.801)
Rich obviously didn't get the memo that More is scared out of his mind. In many ways, however, this works against More. No one would care about his opinion if he were just some regular schmo on the street. Instead, his reputation as a staunch moralist makes his opinion even more valuable.
MORE: Don't! If your opinion's what I think it is, it's High Treason, Roper! [...] Will you remember you've a wife now! And may have children! (2.27)
This passage gives us insight into the nature of More's fear. He's not all that worried about what could happen to him, but he is worried about what could happen to Alice and Margaret. It would kill him if something happened to his family because of his actions.
MORE: [...] If the King takes this matter any further, with me or with the Church, it will be very bad, if I even appear to have been in the pay of the Church (2.305)
After resigning from the Chancellorship, More and his family are plunged straight into poverty. It's a nasty scene. Even with this newfound destitution, however, More is still so terrified that he refuses to accept any assistance that could link him back to the Church. Of course, he's also doing this to show that his decisions are his own, and that's an act of bravery.
MORE: (With a sudden, contemptuous sweep of his arms) They are terrors for children, Master Secretary—an empty cupboard! To frighten children in the dark, not me. (2.375)
Oh, wow—More's coming out swinging. Although we know that he's scared on the inside, More puts on a good show of confidence during his confrontation with the shadiest politician in the game, "Crooked" Tommy Cromwell. Of course, More's utter hatred of the guy makes this epic verbal smack-down all the more satisfying.
MORE: (Turns to go, pauses. Desperately) May I see my family? (2.542)
Once again, we see that More's main concern is his family. At this point, he knows he's up the creek without a paddle, but he still holds out hope that his fam will be safe.
ALICE: [...] I don't believe this had to happen.
MORE: (His face is drawn) If you say that, Alice, I don't see how I'm to face it. (2.650-651)
By now, the family has come to terms with reality: More will either be in prison for the rest of his life, or executed for treason. Neither is a great option. As for More, he's finally being forced to face the reality of his fears.
MORE: Have patience, Margaret, and trouble not thyself. Death comes for us all; even at out birth. (2.789)
Interestingly, all of More's fears evaporate as soon as he's convicted of treason. No longer is he concerned about legal loopholes or public oaths—he's accepted his fate and almost takes pride in it.