It’s a dog-eat-dog world …is a bit of a cliché. Where does it come from? The first relevant quotation in the OED is from a 5 August 1794 headline in the Gazette of the United States: ‘Dog eat dog’. The next quotation (1822) is from a British source, and then The Times of 30 December 1854 has an example which explains the meaning very well: ‘It was dog eat dog—tit for tat... the customers cheated us in their fabrics; we cheated the customers with our goods.’
Chomp at the bit appears more often in most modern written sources than champ…; Dictionaries make no comment about chomp’s correctness; A small survey suggests that most people would edit chomp to champ; I comment on it in my Fowler, but only one other usage guide does; Insisting that champ is the only correct form seems to be a 'thing'.
The rule seems to be that if a candidate can recite half a dozen policy positions by rote and name some foreign nations and leaders, one shouldn't point out that he sure seems a few whereases shy of an executive order. The above is a superlative example of the creative potential of the idiom frame ‘a few X short/shy of a Y’, e.g. ‘a few fries short of a Happy Meal’. As a further historical footnote, it is interesting that the legalistic, ritual use of whereas as a preamble to legal documents led to its being used as a noun, defined as follows in the Urban Dictionary of its day, Grose’s 1796 Classical Dictionary of the Vulgar Tongue: