Relative+absolute positioning is your best bet:

#header {
  position: relative;
  min-height: 150px;
}

#header-content {
  position: absolute;
  bottom: 0;
  left: 0;
}

#header, #header * {
  background: rgba(40, 40, 100, 0.25);
}

<div id="header">
  <h1>Title</h1>
  <div id="header-content">And in the last place, where this might not be the case, they would be of long standing, would have taken deep root, and would not easily be extirpated. The scheme of revising the constitution, in order to correct recent breaches of it, as well as for other purposes, has been actually tried in one of the States.</div>
</div>

But you may run into issues with that. When I tried it I had problems with dropdown menus appearing below the content. It's just not pretty.

Honestly, for vertical centering issues and, well, any vertical alignment issues with the items aren't fixed height, it's easier just to use tables.

Example: Can you do this HTML layout without using tables?