Lyrics in question:
Let's take this moment to establish a precedent
First of all, sir, we won't involve you in this
Imagine this debate with all of congress, it's ruinous
I'll reassure the South, 1808 is still the year
That was agreed upon
That buys us time and assuages fear
I'll tell the North that on January 1st
Of that year, we'll ban importation handling the worst
Once I get all this agreed upon, I'll pick up a pen
And introduce a motion never to discuss this again
Though I am neither young (you are on my lawn), nor hungry (just ate), and only dubiously scrappy, I shall not throw away my shot to answer this question.
The short answer is that Congress did not table all discussion of the slave trade until 1808, though it's true that some members suggested at various points that even debating the question before 1808 was unconstitutional, to say nothing of premature, but they debated it anyway. That got going less than two full weeks into Washington's first term, initially over the ten dollar tax that Congress was permitted to levy per head on enslaved people imported to the United States. The question arose also in response to antislavery petitions and with regard to the carrier trade, importing slaves from Africa to a third country by Americans and on US-flagged ships. The first law passed regarding that date to 1794. There's a second round, with debates, in 1800, then debates but no action in 1805. That last is in response to South Carolina re-opening the trade that year. Then at the end of 1806, Thomas Jefferson recommends action taken to go into effect on January 1, 1808 and the ball really gets rolling. It's law
The long answer is one of my longest, and that's saying something. :)