I actually do remember hearing Dropkick Me Jesus on the radio when it first came out. This was before folk music stations regularly played on the East Coast, but I was living in St. Louis where they did. It was a real song, but I'm sure the authors (and the audience) understood the campy, tongue-in-cheek slant was done purposefully. Another in this vein was the wonderful Country hit How Can I Miss You, When You Won't Go Away?

But there have indeed been songs I remember whose lyrics were so bad--they were such howlers--that to me they'll always be classics. Most of them, predictably, were written by immature songwriters at the dawn of the rock 'n roll era. One in particular that comes to mind was Patches, a 1962 "tragic" pop ballad by Dickey Lee. It was a real groaner about a guy who wouldn't date a poor girl because his mom and dad wouldn't let him -- so of course she kills herself. (Riiiight.)
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PATCHES
by Dickey Lee (Royden Dickey Lipscomb)

Down by the river that flows by the coal yards
Stands wooden houses with shutters torn down
There lives a girl everybody calls Patches
Patches my darling of Old Shantytown.

We planned to marry when June brought the summer
I couldn't wait to make Patches my bride
Now I don't see how that ever can happen
My folks say No, and my heart breaks inside.

Patches oh what can I do
I swear I'll always love you
But a girl from that place would just bring me disgrace
So my folks won't let me love you.

Each night I cry as I think of that shanty
And pretty Patches there watching the door
She doesn't know that I can't come to see her
Patches must think that I love her no more.

I hear a neighbor tellin my father
He said a girl name of Patches was found
Floating face down in that dirty old river
That flows by the coal yards in Old Shanty Town.

Patches oh what can I do
I swear I'll always love you
It may not be right But I'll join you tonight
Patches I'm coming to you.
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He wouldn't date her because Dad wouldn't like it, but of course, he's quite willing to kill himself when she does - typical maudlin teenage boo-hoo sentimentality. HERE it is, if you want to howl along.

In a related vein, my memory holds a treasury of individual fat-headed lyric lines and other groaners. An example is the Beatles' "Fun is the one thing that money can't buy." (Oh, really?)

Then there were other lines that are bad on their face, but in context are very clever and I think they're great, like The Turtles' "Eleanor, gee I think you're swell, And you really do me well, You're my pride and joy, et cetera."

Love it. :-)