That's an interesting hypothesis. Is this the case nationwide or just in your neck of the woods?
Comparing and contrasting the respective parties' platforms, one would be hard pressed trying to resolve their differences on "social issues" such as abortion, drugs, conscription and police powers to the satisfaction of many on FreeRepublic, let alone the general population.
Aside from both parties' opposition to undeclared pre-emptive wars and higher taxes to fund them, I see little commonality.
Perhaps this move to the Constitution Party you observe is done to support a particular candidate?
That was the primary sentiment expressed by conservatives when the LP got so shafted in 2000, though where they actually landed is not known to me. I believe the liberal faction that showed up in 1996 stayed on to make the party an adjunct to the Democrats in function if not name.
True, the Constitution Party differs from the Libertarians on approach but come close on eventual goals. I believe their platform is noble and should be examined by Republicans rendered aimless by corrupt influences.
No particular candidate, just no pseudo-conservatives like John McCain (who will probably be the Republican candidate). Nothing more comforting than a new face leading us down the familiar road of ruin, is there? God help us all.