Had they not seceded, the Morrill tariff would not have passed. They had the votes to defeat it.
What was the result of the vote in the House of Representatives?
The South did not have the votes to stop it once the newly elected Senate took office even if no Southern state had seceded. Here, as posted by former poster GOPCapitalist in 2003, is the vote calculation by Texas Senator Louis Wigfall who outlined his vote calculations on December 12, 1860 before any state had seceded. It deals with Lincoln's nominations in the future Senate, but it applies equally well to the Morrill Tariff vote.
"Tell me not that we have got the legislative department of this Government, for I say we have not. As to this body, where do we stand? Why, sir, there are now eighteen non-slaveholding States. In a few weeks we shall have the nineteenth, for Kansas will be brought in. Then arithmetic which settles our position is simple and easy. Thirty-eight northern Senators you will have upon this floor. We shall have thirty to your thirty-eight. After the 4th of March, the Senator from California, the Senator from Indiana, the Senator from New Jersey, and the Senator from Minnesota will be here. That reduces the northern phalanx to thirty-four...There are four of the northern Senators upon whom we can rely, whom we know to be friends, whom we have trusted in our days of trial heretofore, and in whom, as Constitution-loving men, we will trust. Then we stand thirty-four to thirty-four, and your Black Republican Vice President to give the casting vote. Mr. Lincoln can make his own nominations with perfect security that they will be confirmed by this body, even if every slaveholding State should remain in the Union, which, thank God, they will not do."