The Daily Dish, often a conduit for linguistic prescriptivism (see here), also displays its fair share of awkward and questionable linguistic practices. Take the following modal verb coordination as a case in point:
"Megan believes the government shouldn't and can't successfully refinance people's mortgages."
I find the coordination of shouldn't and can't syntactically awkward and semantically ill-formed (or is it the other way 'round?). The traditional, Linguistics 101 explanation of modal verbs is that they express possibility and necessity. Typically, the modal should expresses a level of necessity in that it means one is obligated to some extent to perform the action under question. However, the modal can is highly ambiguous between a possibility and necessity reading. So, the sentence you can jump is ambiguous between you are allowed to jump and you have the physical ability to jump. In the absence of disambiguating information (such as Gricean pragmatics), I have no default or preferred interpretation (perhaps you do). My impression is that there is also a register difference between shouldn't (high) and can't (low). So my reaction is driven in part by the contrasting functions and registers of shouldn't and can't.
Am I alone in this interpretation? Let's see. Being a corpus linguist at heart, I went to the data. I performed a Google search to determine the frequency of the relevant collocations (for a nice discussion of why I should NOT use Google for this kind of thing, see Kilgarriff's Googleology is Bad Science, but I'm a blogger, so screw it, haha):
4,290,000,000 for can
1,630,000,000 for should
1,410,000,000 for could
692,000,000 for can't
617,000,000 for cannot
81,000,000 for shouldn't
'shouldn't and X'
46,400 for shouldn't and can't
7,140 for shouldn't and cannot
2,630 for shouldn't and couldn't
2 for shouldn't and can not
1 for shouldn't and could not
'should not and X'
276,000 for should not and cannot
53,200 for should not and can not
52,600 for should not and could not
30 for should not and can't
No results found for should not and couldn't
'should and can'
703,000 for should and can
'should and could'
365,000 for should and could
7,160,000 for can and should
1,360,000,000 for must
340,000,000 for shall
107,000 for can't and shouldn't
291,000 for should and must
36,200 for should and shall
Results: I included the base modals and their collocations to round out the picture of the overall frequency of these words. Many other searches could have been performed to provide an even more complete picture of the frequencies of modals. The mini-data here show that should and can is the most frequent collocation. Sullivan's shouldn't and can't is the fourth most frequent negated collocation.
Discussion: Given the low frequency of Sullivan's collocation, plus the high frequency of the non-negated version, plus the high frequency of can't alone, I take this to be evidence that his phrase is generally dispreferred (i.e., I am not alone). The large difference in the base-form collocation should and can (703,000) and the negated version shouldn't and can't (46,400) is interesting. It is worth noting that most of the negated versions were in roughly the same range as shouldn't and can't (with the high frequency should not and cannot exception).