According to karoll at Crooks and Liars ("Sarah Palin Wonders Aloud if Libya Action is a 'Squirmish'", 3/29/2011):
Madam Malaprop, thy name is Sarah Palin. [...] Called in by Fox News to deconstruct President Obama's speech, she wonders aloud whether the Libya action is a war, an intervention or a "squirmish".
And so she does, at about 0:21 of the Fox News clip below:
More exactly, the passage is:
And you know, another big question that has to be asked, Greta, is "Are we at war?"
I- I haven't heard the president say that we are at war,
and- and that's why I too uh am not knowing
do we use this- the term 'intervention', do we use 'war',
do we w- use uh 'squirmish', what is it?
Let's start by stipulating that squirmish aptly describes the way many people feel about the fighting in Libya. Because of this, and because of Sarah Palin's star power, it may well gain currency in a sense that is closer to the first Urban Dictionary entry ("A verbal stoush between two or more parties that is so petty, pointless, misinformed or ill-conceived that it makes witnesses wince with embarrassment, or so uncomfortable that they don't know where to look") than to the Wordnik entry ("showing signs of restlessness resulting from feelings of discomfort or distress"). Though of course the current fighting is Libya is in fact serious and bloody enough, and I certainly hope for a good outcome.
But is it likely that Ms. Palin intended this witty coinage? or that this was really a clasical malapropism, meaning that she has lexicalized skirmish in error as "squirmish"? I doubt it. A more likely theory, I think, is that this is a speech error of the type know as perseveration: the repetition of an onset segment from an earlier word in a later one.
She offer three possible terms, "war", "intervention", "skirmish". And as evidence that the initial /w/ of "war" has not been adequately inhibited, note that she starts to insert /w/ into the onset of "use". In that case, she catches herself and suppresses it quickly, perhaps because neither /yw/ nor /wy/ is a possible English syllable-beginning. But it immediately pops up again in the onset of "skirmish", slotted into the syllable-initial consonant sequence in the only place English phonotactics allow it to go.
Here's the critical sequence, at normal speed and then slowed down by a third:
Unfortunately, many Americans live on the outsquirts of hope.
Here again, it seems unlikely that LBJ either meant this as a witty coinage, or had genuinely mis-lexicalized outskirts as "outsquirts". (Though there are a few jokey cases of "outsquirts" as an eggcorn for outskirts, e.g. here.) And in LBJ's 1964 performance, there's no obvious disfluency, nor is there any priming of an onset /w/ in the previous sentences. It's conceivable that the labial constriction for the offglide of "out" is held through the onset of "skirt", though as far as I know this is not a common kind of speech error.
However, this passage occurs just before a subordinate climax introducing the "War on Poverty":
Unfortunately, many Americans live on the outskirts of hope — some because of their poverty, and some because of their color, and all too many because of both. Our task is to help replace their despair with opportunity.
This administration today, here and now, declares unconditional war on poverty in America. I urge this Congress and all Americans to join with me in that effort.
It will not be a short or easy struggle, no single weapon or strategy will suffice, but we shall not rest until that war is won. The richest Nation on earth can afford to win it. We cannot afford to lose it. One thousand dollars invested in salvaging an unemployable youth today can return $40,000 or more in his lifetime.
So it's possible that "war" was primed for LBJ, just as it was for Sarah Palin, and imposed its initital labiovelar on an available /sk/ onset.
One odd thing — there are zero Google hits at present for "outsquirts of hope". Either this is because no one cared to make anything of LBJ's slip, back in those less partisan days, or because without the internet, the jokes and jibes were evanescent.