I also have been searching for this forever. I've found a couple of different recollections of it and combined with what I remember, I think thie is it.

The Spaniel by Edgar, Al & Moe.

Once upon a midnight cautious, while I pondered weak and nauseous,
Over some advertising copy I had wrote for Macy's store,
While I nodded, nearly napping, suddenly there came a yapping,
As of someone loudly yapping, yapping at my office door.
"'Tis some client there," I muttered, "Yapping at my office door.
Only this and nothing more."

The I felt my terror worsen, for my guest was not a person.
In there stepped a cocker spaniel. Naturally I jumped in fear.
Tried to climb an oaken panel, ripping there my new grey flannel,
But the spaniel merely stood there, speaking out in voice so clear,
Speaking out like Jack Lascoulie in a voice both loud and clear;
Quoth the Spaniel, "Drink Blatz Beer."

How I marveled this ungainly dog who did commercials plainly,
How he spoke the message clearly, selling points he underscored.
For I could not help agreeing that no living human being
Ever yet could mouth a slogan without sounding slightly bored.
Most annnouncers being human can't help sounding slightly bored.
Quoth the spaniel, "Buy a Ford."

Thus this dog with voice like Murrow made my heavy brow unfurrow,
Thoughts of fortunes I could make now made me shake down to my knees.
But the spaniel set me grieving then by turning tail and leaving.
Naturally I begged him tarry, crying out, "Stay with me, please."
Chasing him along the hallway begging him, "Stay with me please."
Quoth the spaniel, "Eat Kraft Cheese."

Long live Mad Magazine.