It is difficult to pin down the definition of "libertarian" but to me, a libertarian government is one that is created as the minimally necessary instrument to protect peoples' rights. The raison d'être of libertarian government is the protection of individual rights.
Governance is the necessary evil by which the protection of individual rights is accomplished.
The Constitution, in contrast, is an exercise in creating a representative government. Not one whose animating purpose is to protect the rights of the people, but one that has a general mandate to govern, within specific domains, and derives its legitimacy from the consent of the people.
It is illustrative to read Federalists Nos. 9-10. http://thomas.loc.gov/home/histdox/fed_09.html, http://thomas.loc.gov/home/histdox/fed_10.html. It's a defense by Madison and Hamilton of republican government, intended to counter critics who asserted that republican government must inevitably lead to anarchy. In Federalist No. 10, Madison addresses the question of how a republican government deals with factions that want to trample the rights of others:
"If a faction consists of less than a majority, relief is supplied by the republican principle, which enables the majority to defeat its sinister views by regular vote. It may clog the administration, it may convulse the society; but it will be unable to execute and mask its violence under the forms of the Constitution. When a majority is included in a faction, the form of popular government, on the other hand, enables it to sacrifice to its ruling passion or interest both the public good and the rights of other citizens. To secure the public good and private rights against the danger of such a faction, and at the same time to preserve the spirit and the form of popular government, is then the great object to which our inquiries are directed."
Madison's answer to the latter question is not an appeal to rights enforced by courts, but to republicanism--the idea that elected officials will insulate public policy from the ephemeral whims of the majority:
"A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking."
The posture of Federalist Nos. 9-10 are clear: Hamilton and Madison are making the case for representative, republican government. They do consider the issue of individual rights, but in the context of explaining how rights can be nonetheless protected in a representative government. A libertarian government, at least as I understand it, approaches the question from the opposite direction: the protection of individual rights is the first and foremost concern, and sole purpose, of government.