Big government in what way? How was it manifesting itself in 1860?
In more liberal groups like the Republican party for example. Keep in mind when studying the civil war that the republican party back then was the liberal party and supported a larger role for government, whereas the democrat party was the conservative party and supported states rights and lower taxes.
The election of Lincoln freaked out so many people in the south because he was from this new liberal party (of which so many south-haters were members and supporters of btw) which was created in the north and really had mostly northern interests in mind. Also, if you look at the electoral map of 1860, you will see that it was a purely sectional election of a sectional party. The only states that voted for Lincoln were northern states. Not a single southern state voted for him. When the south saw that this new liberal pro-tarrif party with really only sectional interests in mind had been elected, they had good cause for concern.
And don't underestimate the money issue here. While Lincoln had stated in his inaugural address that he had no intention of passing any laws against slavery, his party was a pro-tariff party and he had campaigned in certain northern states on the tariff issue. The North was of course all in favor of tariffs to protect their industry. The South, however, being more agricultural and needing to import many of their goods, hated the tariffs. South Carolina almost seceded over tariffs in the 1830s. The republican party in 1860, however were planning a new high tariff which they were trying to pass through congress which would increased the effective rate collected on dutiable imports by approximately 70%. This was much higher than the tariff proposed in the 1830s which South Carolina almost seceded over. Charles Dickens published a lengthy article in 1861 saying:
"If it be not slavery, where lies the partition of the interests that has led at last to actual separation of the Southern from the Northern States? …Every year, for some years back, this or that Southern state had declared that it would submit to this extortion only while it had not the strength for resistance. With the election of Lincoln and an exclusive Northern party taking over the federal government, the time for withdrawal had arrived … The conflict is between semi-independent communities [in which] every feeling and interest [in the South] calls for political partition, and every pocket interest [in the North] calls for union … So the case stands, and under all the passion of the parties and the cries of battle lie the two chief moving causes of the struggle. Union means so many millions a year lost to the South; secession means the loss of the same millions to the North. The love of money is the root of this, as of many other evils... [T]he quarrel between the North and South is, as it stands, solely a fiscal quarrel."