The article directly addresses this: >"In the end, they all voted to remove McCarthy. Many people wondered afterwards why McCarthy did not offer the Democrats

The article directly addresses this: >"In the end, they all voted to remove McCarthy. Many people wondered afterwards why McCarthy did not offer the Democrats a bargain in order to sustain him. The answer is that the logic of the procedural coalition wouldn’t allow it. As with the Speakership vote in January, McCarthy didn’t need one vote, one time. He needed an ongoing procedural coalition. Unless the Democrats were going to form a permanent alliance with him, saving him on the vacate vote wouldn’t have done any good. In fact, it would have simply turned more Republicans against him, as whatever concessions he gave the Democrats would have certainly moved policy to the left." So it either had to be a fully negotiated, lasting alliance for the rest of this Congress, or nothing. McCarthy did not make any moves towards such a thing, completely contrary to your assertion that they'd "have him by the balls". On the contrary right after the vote for the CR he immediately went on TV Sunday to try to backstab Democrats and (preposterously) say they were at fault.