Since every blogger interested in doing so has by now posted their opinions about the future of the Republicans I might as well add my own view.
Right now the Republican party is a motley alliance of "conservative" factions: social conservatives, neo-conservatives, fiscal conservatives and minor scatterings of libertarians, isolationists, goo-goos, supply-siders, etc. If the party reforms by one faction rising to dominant ascendancy it will be too small to be competitive as a major party. The task, as I see it, is to find unifying principles acceptable to most of the factions.
One bit of good news is that the neocon faction will probably remove itself in order to infiltrate the new dominant party. They always were first and last power-seekers loyal only to their foreign policy agenda.
Perhaps the remaining factions can agree to a revived emphasis on law and order. This could include the belated recognition that terrorists are best understood as criminal, not military, enemies. There should also be renewed respect for Constitutional provisions such as habeus corpus, prohibition on warrantless searches and the duty of Congress to exercise oversight of the executive and to bear the responsibility of declared warfare. The Department of Justice must be shielded from attempts to use it for partisan purposes. Much of this is easier to advocate for the party not in power and all of it should be worthy of support by anyone claiming to be a conservative.
I believe a focus on such issues would be beneficial to the Republican party and, more importantly, for the country. We need an effective loyal opposition.