The expression "a thousand times" is a well-known and very old exaggeration (hyperbole). "No, comrades, a thousand times no!" is simply an example of the use of this literary and rhetorical device. It has no independent origin. "A thousand times" is merely emphatic, and thus it is not surprising that it is found across many languages.
De:1:10: The LORD your God hath multiplied you, and, behold, ye are this day as the stars of heaven for multitude. De:1:11: (The LORD God of your fathers make you a thousand times so many more as ye are, and bless you, as he hath promised you!)
"The Arabian Nights'entertainments" 1808:
I consider my kingdom, great and powerful as it is, as of no value, when I have the pleasure of seeing you, and of telling you a thousand times how much I love you.
"Letters to a Prebendary" John Milner - 1800:
... my History, and by common place topics of misrepresentation and calumny against the religion of our ancestors under the illiberal and abusive term of Popery (1); such as have been a thousand times urged, and a thousand times refuted.
The OED gives it the status of a phrase and dates its origin to the very late 19th century, but I cannot see that the phrase is anything other than an adaptation:
- a. Often used vaguely or hyperbolically for a large number: cf. hundred n. and adj.So ten thousand, thousands, thousands of thousands, thousand and one.
c1000 Ags. Ps. (1835) iii. 5 Ic me nu na ondræde þusendu folces.
b. Phrases: a thousand times, no: certainly not; similarly a thousand times, yes (rare); I believe you, thousands wouldn't (and similar expressions): ambiguous responses to remarks received with scepticism; death of (or by) a thousand cuts: a succession of minor hurts that are cumulatively very serious or annoying; ...
1896 ‘M. Rutherford’ Clara Hopgood v. 57 ‘No,’ said Madge, ‘a thousand times no.’
1897 H. James Spoils of Poynton xxii. 279 A thousand times yes—her choice should know no scruple.