When the Republican party changed their primary system to foster longer, more drawn out primaries, what they had in mind was probably the Hillary - Obama war that raged on throughout 2008 and gave Obama a huge advantage in the general election in that he had already done groundwork in most states. What they definitely did not have in mind, is the cannibalistic blood bath now occurring on the right which is no longer threatening to weaken the eventual nominee, but is now overtly doing damage to the party's chances. (note: for the rest of this post I'm basically assuming Romney is the eventual nominee, if that somehow doesn't happen, then the extended primary has hurt the party by nominating someone in this field other than Romney).
The first signs of trouble started last week before the Iowa Caucuses when Mitt made the strange and probably unnecessary move of coming out against the DREAM ACT the day before the Caucus, vowing to veto it if it came to his desk as president. The move came too late to probably make any difference in Iowa (with an 8 vote margin you could make a case that it made the difference, if you think Mitt narrowly getting 2nd would make a difference) but is a very damaging move for the general election, where the Republicans badly need to start winning over Hispanic voters or risk obsolescence.
The proverbial dyke started to crack with the now famous gaffe "I like to be able to fire people." This is a perfect example of the old Washington saying: "a gaffe is when you screw up and accidentally tell the truth." This wound was self-inflicted and a longer primary greatly increases the chances of this kind of gaffe happening because it'll keep Romney on the ground, campaigning in person, where he's liable to slip up, rather than campaigning via tv ads which Romney is greatly looking forward to.
The dyke burst when the other Republicans used this gaffe to open up the Bain Capital line of attack against Romney. This is where the situation turns dire from the Republican party's point of view. Team Romney has to be furious that they're having to answer these attacks from Republicans. They were expecting Democrats to say these things, and I have zero doubt that they were laying in wait, convinced that they could turn this into a winning issue by calling Democrats anti-capitalists and shouting "Socialism!" "Fascism!" at the top of their lungs for months (to Republican candidates like Santorum, socialism and fascism are apparently the same thing). Now the Democrats will take a different tack in the general election, they will use the footage of Romney's rivals articulation of this attack, instead of having to make the attack themselves. This eviscerates the Romney camp's rebuttal because now they have to address this issue on substance and can no longer call the attack radical as it is bi-partisan.
None of this is as bad for the party as the catastrophe about to happen in South Carolina. Newt's SuperPAC has apparently already bought $3.4million in air time in the palmetto state and ostensibly plans to spend nearly all of it on anti-Romney attack ads emphasizing the Bain Capital - "Vulture Capitalist" line of attack. You don't have to be a political scientist to realize that a $3.4M dump in 2 weeks time with these viscous (and largely true) attack ads will diminish a candidate's favorability. The danger is that such intense anti-Romney push has a good chance of sticking. Unlike the general election where a candidate is campaigning everywhere and can pour resources into a place where its taking a beating, the Romney campaign will have to move on from South Carolina after the primary with little opportunity to repair his brand there until the general election starts. This is particularly dangerous because Romney is already relatively unpopular in the South and according to some polls is already trailing the president in a head-to-head match-up in SC. Newt's $3.4M in-kind donation to the Obama campaign in SC will likely put that state in play and minimally will force Romney to spend money and time there on defense during the general election to repair his reputation. South Carolina is just the beginning, Romney's unfavorables are so bad in places like Texas and Arizona that further missteps risk putting even these states into play as well, remember, Obama doesn't have to win these states necessarily, but if Romney has to play defense there, then he can't be on offense somewhere else.