Note that one may admit to having been drunk, but to be called drunk is quite offensive. Even the dysphemisms, like legless, are somehow gentler than the straight word. Meanwhile I'm not sure whether we'd rather have our politicians sober but prone or upright but merry.
A lot of people persist in thinking that Sir Nicholas Scott, found lying on a Bournemouth pavement, was drunk, but none of the reports I've seen actually used the word. Some said he was "the worse for wear", but drunk, no. My Roget's Thesaurus offers well over 100 synonyms, roughly graded by degree of squiffiness, from merry, tiddly and half-cut through smashed to paralytic. Even discounting some expressions found nowhere else, like pot-valiant and stocious, it's an impressive total. There was a nice euphemism last week in the letters columns of the Daily Telegraph. Was there anyone in his constituency association, asked a Scott supporter, who could say that they had never "fallen prey to the lure of Bacchus"? But the ultimate euphemism is surely wonderful. ("Was I drunk?" - "You were wonderful.") Only sex has more periphrases.