Akademik

с душком
С ДУШКОМ coll
[PrepP; Invar; subj-compl with copula or nonagreeing modif]
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1. [subj: a noun denoting food]
not fresh, decaying:
- X с душком{{}} X is going bad;
- X is spoiling;
- X smells bad (like ift going bad).
     ♦ Выброси эту рыбу, она с душком. Throw out this fish-it's going bad.
2. с (,каким) душком disapprov [subj: human, collect, or abstr; while in Russian the modifier may be only implied, the English equivalent in most cases will specify it]
(used to show that the speaker thinks the views of some person or group, the direction taken by a newspaper, some theory etc has a tendency to be ethically, politically etc wrong; in the Soviet context was also used to show that some phenomenon contradicted official ideology) sth. is undesirable, harmful, marked by some unacceptable (as implied or specified by the context) tendency:
- X с (нехорошим) душком{{}} X has a nasty smell to it;
|| X с либеральным (консервативным, антисемитским и т. п.) душком{{}} X is tainted by liberalism (conservatism, anti-Semit ism etc);
|| X с сомнительным душком{{}} X has a dubious (doubtful) air (about it <him etc>).
     ♦ ...Преуменьшать значения молитвы... нельзя. Далеко зашел старик. С душком, с нехорошим душком молитва (Абрамов 1). ...The importance of the prayer could not be underestimated. The old man had gone too far It had a nasty smell to it, that prayer (1a).
     ♦ ...Он [отставной активист] высказался в том духе, что... квартира в жилтовариществе советских фотографов превратилась в пристанище для сборищ с определённой подкладкой, с сомнительным душком (Аксенов 12). ...The retired activist expressed himself to the effect that...an apartment in a housing community for Soviet photographers has been "turned into a haven for gatherings of a certain element, with a dubious air" (12a).

Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. . 2004.