change the number to a string before parsing:
var responseData = JSON.parse( strJson.replace(/\: (\d{17,}),/g,': "$1",') );
Please note that this will lead to a false change in any string data that contains a large number that looks like a json value, but I would call it a worthy compromise compared to deep investment alternatives. however, this is not just a large number that hits, but (":" + theNumber + ","); the only time I can imagine what is happening is someone “repeating the tweet” of the JS invalid API response. use a parser if you care about being perfect.
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