The Mills Brothers' "Too Many Irons in the Fire"

This morning I listened to the first disc of the Mills Brothers' The Anthology (1931-1968).  Even though I wasn't transcribing the lyrics, I noticed a small grammatical thing about the lines "Oh, it’s too bad your one fault will keep us apart / This fault is breaking my heart" in “Too Many Irons in the Fire.”

The second of those lines can be parsed two different ways; the key difference is "is breaking," which could be either a linking verb and a gerund or a present progressive verb.  The different grammatical structures create different meanings for the line.  Parsed as a linking verb and a gerund, "breaking my heart" is the "fault."  That line could be rendered as "This fault = breaking my heart."  Parsed as a present progressive verb though, the fault itself isn't named*; the significance is only that it's affecting the speaker/singer.  As a simple present tense (instead of progressive), it could be rendered as "This fault breaks my heart."

I think the second parsing (as a present progressive) has a slight advantage in that it doesn't specifically name the fault, almost as if the singer/speaker doesn't want to deal with it.  Instead of naming the fault, a few positive qualities are mentioned in the immediately-preceding lines:

You have two beautiful eyes
Eyes that I idolize 

You have such charms in your tresses
Two perfect arms for caresses

I also mention this so I can point out the almost-palindromic assonance with "eyes"/"-ize" and "I"/"i-" in "Eyes that I idolize."

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*I should note that it isn't named in that section.  The fault itself seems to be in the title and the first lines: "Too many irons in the fire / And there's too many loves you desire."