Ok, well I'll just post this as a solution for anyone who may be
interested. Here are the steps I am taking:

1. Set up your mail merge as usual
2. Use styles as a way of determining what text you need to resize.
For instance, I have a field called 'Name' that is what I am worried
will require resizing. So I created a style and used it exclusively
for this field.
3. Merge to a new document
4. In this new document, add this code to the VBA editor:

Public Sub PrintParagraphsToFormat()
Dim para As Paragraph
For Each para In ActiveDocument.Paragraphs
If para.Style = "INSERT THE STYLE NAME YOU CHOSE HERE" Then
para.Range.Select
While (IsTooLong(para))
Selection.Font.Size = Selection.Font.Size - 1
Wend
End If
Next
End Sub

Public Function IsTooLong(para As Paragraph) As Boolean
Dim rng As Range
Set rng = para.Range
Dim iHeightFront As Integer
Dim iHeightEnd As Integer
iHeightFront = rng.Information(wdVerticalPositionRelativeToPage)
rng.Collapse (WdCollapseDirection.wdCollapseEnd)
rng.MoveEnd Unit:=wdCharacter, Count:=-1
iHeightEnd = rng.Information(wdVerticalPositionRelativeToPage)
IsTooLong = iHeightFront iHeightEnd
End Function

What this code does is iterate through each paragraph in the document,
and check the style that is applied to that paragraph. If it matches
the one in question, then it checks the vertical position before and
after the paragraph. If these two values are not the same, then the
text must be wrapping to another line. So it lowers the font one size
at a time until the text fits on one line.

This is not a generic, pretty solution, but hopefully will help someone
get started.