Nonsense. First, if the south was so against tariffs, they could have easily blocked them in Congress if they had stayed. But the south was not even uniformely opposed to higher tariffs.
And I'll ask once again. Did England and/or France impose tariffs on American cotton? Did American tariffs, high or low, have any impact on the market price of cotton?
That is false. Every southern state was present for the vote in the House, and it passed on a strictly sectional breakdown. I believe only one southern congressman voted yes.
As for the senate, it is a similar falsehood that they could have blocked it beyond March 1861 even if every southerner had remained and voted no. I have the vote data itself printed out at home and will happily provide you with its details if you desire, but the situation they faced was essentially this:
In January 1861 Kansas was admitted as the 34th state, giving the senate 68 members total. That meant that, at a bare minimum and presuming all senators were present, it would take 34 yes votes for the Morrill tariff to pass plus a tiebreaker by Republican vice president Hannibal Hamlin (This could have potentially been delayed for some time by parliamentary tactics but not indefinately and, as I will note shortly, most of those tactics had already been exhausted).
The incoming senate that took office on March 1861 had, IIRC, 31 Republican members - up from around 27 or 28 in the previous session thanks to a change in some seats and the 2 new Kansas senators. That means 31 yes votes were virtually guaranteed and they would have to gain 3 others, or take advantage of a mid-term vacancy, to pass the bill. Now lets assume the south never left and everything continued business as normal after March. Of the northern democrats, one came from the strongly pro-tariff state of New Jersey and may be generally predicted to have voted for it. A second from Delaware was absent the day that the real vote happened but his earlier speeches indicated how he would determine his vote. He offered to vote for the bill on the condition that a single amendment that benefitted his state would be added, so his vote could have been obtained. That puts us at 33.
Of the remaining northern democrats it is a bit harder to determine how they would have voted. Three we can fairly safely say would have voted no: Stephen Douglas of IL, Jesse Bright of IN, and one other who indicated his opposition (I believe he was from minnesota). The west coast democrat senators, a constitutional unionist from Missouri, and a couple others are harder to determine. But a couple scenarios are indeed possible.
1. One of the California senate seats was vacant briefly in mid 1861 after they took office in March. This would have meant that 67 members were present instead of 68, so simply getting 1 more vote would have given a clear majority and passed it without even a tiebreaker.
2. Stephen Douglas died in June 1861 and was replaced with a Republican, which would have given them 34 votes.
3. One of the undetermined northern democrats and others - could either have been for it already, or could have been swayed either by cutting a deal with him etc. Lincoln indicated that he was intent upon doing this a few months earlier in his speech at Pittsburgh, where he pledged to make the tariff - if unpassed by March - his top legislative priority.
But the south was not even uniformely opposed to higher tariffs.
That too is false. For all practical purposes, the southern governments were dominated by free traders. Protectionists were a small minority. This is evidenced in the House vote, where only one single southerner voted yes. In the senate only one southerner could be counted on to have supported it as well - John Crittenden of Kentucky, a Henry Clay protege - and his term ended in 1861 when John Breckinridge took office.