As noted in the WSJ, there is a very small movement afoot to institute something like the Whigs of old in the present. Generally speaking, the group(s) model themselves as a centrist party–more or less free market and socially liberal. But this sounds like the libertarian party.
The Modern Whig Party was the brainchild of soldiers tired of the bickering that filled chow-hall TV screens on bases in Iraq and Afghanistan. One of them, Capt. Mike Lebowitz, a Washington lawyer then serving with the 101st Airborne Division, emailed his buddies and began talking up the idea of a party that would be fiscally conservative, socially liberal and generally mild-mannered. They picked the Whig name because of its ties to the Founding Fathers, William Henry Harrison and the early career of Abraham Lincoln.
The Whigs have a somewhat important, if brief, history. One of the best books on the topic, is Howe’s The Political Culture of the American Whigs. The Whigs were a party that believed, essentially, in the free market, but were not adverse to using government funds for national improvements (roads, canals, etc). The Whigs also believed in the supremacy of the legislature, and did not think that a too strong executive would be good for a properly functioning government. This is why they opposed the “monarch” Jackson.
IF we are including Abraham Lincoln into this mix, they were also no social liberals. Lincoln believed that nature taught certain moral truths that humans were obligated to respect. At the time–the 1830s-40s–the Whigs were less interested in laissez faire economics. That would be the Democrats’ position. The Whigs believed in the more centralizing forces concerning ecnomics and improvement. Yet, the Whigs believed in banks more than the Democrats.
The new Whigs are a far cry from the old Whigs. If they are to emulate a central principle of Whiggish ideology, though, they need to favor a mixed constitutional system more, over a system of deference to the Executive.