Here's how the ballad suggests his reaction:
* He's warned by his "good" wife: "O I saw the king's own hand / And it was writ with a braid / And he said, 'Sir Patrick Spens, / O come and sail with me!'" This indicates the letter is a royal summons, and his wife knows the danger it holds.
* He reluctantly accepts: " 'I'll set sail, my lady, / Though I should sail alone. / But I'll come back to you, / Though I should sail to the deep.'" This suggests that he feels obligated to answer the king's call, even though he knows it could be fatal.
* His final farewell: " 'My boys, my boys, / I'll give ye the best of wine; / And all the gold that's in my house, / It shall be yours this night!' " This reflects his knowledge that he might not return, so he gives his crew a final gift.
Overall, Sir Patrick Spens's reaction is a mixture of dread, duty, and a sense of resignation. He knows the danger of sailing with the king, but he feels compelled to go.