From Wenkang's Qing-dynasty 《儿女英雄传》 chapter 5: 我既这等苦苦相问,你自然就该侃侃而谈,怎么问了半日,你一味的吞吞吐吐,支支吾吾 — 'I've pressed you so hard, you should speak openly; why have you spent the whole time hesitating and mumbling?' The idiom pairs naturally with 吞吞吐吐.
usage
Always negative — implies evasion or guilt. Describes someone trying to dodge a direct question. Common paired with 吞吞吐吐 (hemming and hawing) for emphasis. Often followed by 地 + verb (支支吾吾地说).