Either may be more sensible than pretending that a "big-government" party in 1860 is the same as a "big-government" party today.
Tariffs, a national bank, and internal improvements were all a part of Washington's and Hamilton's Federalist program in the 1790s. They were also all a part of Madison's and Monroe's Jeffersonian Republican policy in the 1810s. To defend a new and weak country and settle its open spaces made some role of the federal government necessary. And a weak federal government would not necessarily have meant greater freedom if state governments did as they pleased.
Radical Jeffersonians or Jacksonians might have taken such policies as "big government," but by today's standards the power and intrusiveness of the federal government under Washington or Madison was negligible. The same was true of Lincoln's initial program, though the requirements of war led both the union and rebel governments to intervene more and more in the lives and finances of the citizenry.
If "big government" meant the same thing in 1860 or 1810 or 1790 as they did today, then we have always been a big government country. Such a conclusion is absurd. The meaning of "big government" was transformed in the 20th century by Wilson, the Roosevelts, Lyndon Johnson and others.
One can certainly disagree about tariffs and internal improvements and national currency, and certainly take objection to high taxes and intrusive government regulation. But to take state sovereignty or near anarchy as the sole standard of true constitutional interpretation is to leave out a large part of American history.
There is a lot of room for a Republican party that supports less government and it will do well, but not if it dumps on or trashes valuable American traditions. If it becomes the party of Calhoun and Jefferson Davis and says that it is the party of freedom, the result would be laughable, and their support will tumble, and rightly so.
It is difficult to precisely draw neat conservative/liberal comparisons between 19th and 21st Century, particularly when talking about something as amorphous as major political party platforms, but if you'll look at the fierce tariff debates from the 1820s on, you'll see that opposition to tariffs was not limited to fighting protectionism but the sure knowledge that when economic growth caused tariff revenues to skyrocket the new found money would not lay around Washington for long. It would be spent; it would be spent to buy votes; it would create power in Washington and dependency in the hinterlands. That is a true conservative principle - and it proves itself a principle because it applies equally today.