Once they resigned their seats in the Congress and the states they represented did not replace them, there was no one from those states to vote down the Morill Tariff bill. In the past and with other tariff bills they were able to stop them by their votes that they cast.
The bill was headed toward adoption in the Senate when Senator Robert M. T. Hunter of Virginia, a free trade advocate, employed parliamentary tactics to delay the vote until the second session after recess. This second session did not meet until after the 1860 election, so the move guaranteed that the tax issue would come up during the campaigns that fall. The Republican party needed Pennsylvania, where protectionist sentiment was strong. The heavy representation of ex-Whigs meant that most leaders favored the American School of government support for industry, banking and transportation
After Nov. 1860.
The Southern cotton states that might have been hurt by the new tariff all had left the Union to form the Confederate States of America. Therefore, they were not affected and did not have a voice in the policies of the country they had renounced. On February 28, the Senate finally voted on and adopted the Morrill Tariff. It was one of the last bills signed by outgoing Democratic president, James Buchanan
(From Wikapedia.)