Republicans are never more dangerous to the cause of liberty than when they are out of power. It is when they are out of power that they might actually attract the support of libertarians, even those who do not have a short attention span.
It is well known that Republicans have a habit of stealing libertarian rhetoric. It is also very well known that Republican follow through is abysmal on that for all the rhetoric they steal they never act on it. Everyone - Republican, Democrat, and Libertarian - knows that is true, although occasionally to score points in a debate Democrats will conveniently "forget" that there is no relationship between Republican word and Republican deed in order to try to paint a false association between Libertarians and Republicans.
When Republicans are in power, the divide between word and deed is apparent to all. There was no libertarian support for No Child Left Behind or Perscription Drug Coverage for Seniors. Libertarians never support deficit spending, following the principle that total spending is equivalent to total taxation. Given that principle, when a libertarian calls for tax cuts that libertarian is also calling for spending cuts by necessity. Direct taxes are evil, but still a lesser evil that the indirect taxes of deficit spending or inflation. When a Republican calls for tax cuts that Republican is calling for more of the burden of taxes to be shifted from direct taxation to indirect taxation.
When Republicans are in power, it is very difficult to paint any sort of assocation, whether by a Republican trying to attract libertarian votes or by a Democrat trying to show a flaw in libertarianism by laying at the feet of libertarianism the faults of Republicans.
But when Republicans are out of power not only is there a shortage of direct examples of how Republicans are nothing like libertarians, that is when Republicans increase their rhetoric theft. There was no rhetoric theft when Bush was trying to defend the use of torture, and there was nearly none when he was trying to justify the baseless invasion of two different countries. There was some effort to portray the invasion as a liberation, but all attempts to paint it as such rang rather hollow.
Such an increased level of rhetoric theft coupled with a decrease in manifest counter-examples leads to some undesirable results. Those who are new to the libertarian movement, or overly forgiving of past betrayals, may be swayed to support Republicans due to the rhetoric, a particularly dangerous temptation given that both are opposing Democrats at that time. Due to having a temporary common cause some might be willing to convince themselves that "this time" the Republicans are actually better. That sometimes leads people away from being libertarian as happened during the Bush administration and the War on Terror. The remaining libertarians, seeing some of their own pulled away have to work twice as hard at trying to win people over since they have to replace those leaving while trying to grow the movement. But even the attempt to persuade people to join is hampered because any attempt to persuade people to support libertarianism is met with opposition by some Democrats who feel more free to create the false association between libertarians and Republicans.
It is when Republicans are out of power that libertarians must most strongly resist thinking well of them, and contine to judge Republicans as harshly as they did when Republicans were in power, acknowledging only the small handful that actually are libertarian because their actions match their rhetoric.