Not entirely sure that I understand what you mean by "break": I'm assuming you want the ellipses to show up (to indicate that the label is longer) vs. simply cutting the text off.
- the ellipses are showing when the label's size is smaller than the text requires
- the label's minSize is about the same as its preferred
- by default, MigLayout doesn't size a component below its min
So you have to explicitly allow the manager to size smaller than the min by overruling the component's min with a component constraint:
content.add(new JLabel("we are looooong and getting longer by the minute"), "wmin 0");
(might be possible on a column constraint as well, didn't check)