Do I need to embargo my dissertation if I submitted portions to journals? It seems that most math journals, including the one I'm submitting to, are very forgiving when it comes to preprints (ArXiv).  But what about dissertations? Will they consider it previously published material?
The general answer is: No, journals don't consider dissertations as previously published materials.

Some exceptions (that I don't know), may exist. If you want to be sure, here's a two things you can do:
1-Verify the instructions to authors.
2-In your letter to the editor that accompanies your submission, state clearly that this manuscript will be part of a dissertation.