And so, at last, we reached the motion of no confidence in Meryl Gravell, but before things could get underway it turned out that the ruling Independent group had cobbled together an amendment to the motion at the last minute as a spoiler tactic.
The chief executive, who had been unusually quiet at this meeting, explained in his best Janet and John voice what this meant in constitutional terms. This boiled down to the unsurprising fact that there would have to be two votes: one on the amendment, and a second on the motion.
The amendment was not available to the public and had not appeared on the published agenda, but from what we could glean in the public gallery, it had been cobbled together to try to make nonsense of the original motion.
A confused discussion followed, with Peter Hughes Griffiths (Plaid), leader of the opposition, reading from the section of the constitution which deals with amendments to motions. The chief executive had ruled that 4 of the 5 parts of the amendment were in order, but this was clearly a generous interpretation.
The council's acting senior legal officer tried to make herself heard, but was interrupted by Pam Palmer. When she was finally heard, she said she felt the first three sections of the amendment were in order (the chief executive had ruled that the first 4 were OK). She was ignored by everybody.
The Independents, led by Cllr Pam Palmer, then decided that they wanted an adjournment. More wrangling ensued, until suddenly the Independents decided to withdraw the amendment. And so the debate got underway.
The substance of the motion was that Meryl Gravell had the other week made some notoriously unguarded comments in public, in which she described people protesting against plans to close parts of the hospital in Llanelli as "rabble" and went on to suggest that the 9,000 people employed by "Mark and me" in the council were less than hard-working and dedicated.
In a good and carefully prepared speech, Peter Hughes Griffiths pointed out that after all the cuts, job losses, downgrades, etc., staff morale was very low. Meryl's words had been a kick in the teeth.
He reminded councillors that she had now been in power for 13 years, and seemed determined to go on for another 5.
Just like Margaret Thatcher in her final, increasingly bonkers years in power, Meryl Gravell seems to be confident that she would go on and on and on (not PHG's words).
Cllr Tyssul Evans (Plaid) seconded the motion. Meryl Gravell had completely lost the plot, he said, and it was time for her to go.
Cllr Huw Lewis, elected as a Plaid member but who now describes himself as an "Independent Welsh Nationalist", rose to speak. He clearly had a lot of scores to settle with his former leader, and set about deploring what he saw as personal attacks. "She has apologised, after all...what's the motivation for this motion? Carmarthenshire deserves better."
Perhaps Cllr Lewis should drop the words "Welsh" and "Nationalist" from his label, and just stick to what he now is: Independent. Anyone who can line up with the likes of Stephen James and his Daily Mail vision of a Merry Englande with a twee Principality attached can scarcely be regarded as a nationalist.
The debate now took a slightly different turn to focus on the demonstration which had triggered the "rabble" remark. Cllr Ken Rees, the lone LibDem (but quite at home with his Tory Independent chums) had felt intimidated. Most of those present, however, felt that the demonstration had been nothing like as bad as Meryl had tried to paint it. As one councillor put it, if things had been that bad, how many people had been arrested?
The question (correct answer: none) went unanswered, of course.
Cllr Siân Caiach gave one of the better speeches, saying that she would be voting on the basis of Meryl's entire record, and not just the remarks made in Llanelli. She pointed out the increasingly undemocratic and opaque nature of the council before citing the latest decision to fund the chief executive's libel case.
Needless to say, that was as far as she got. The chair ordered her to sit down once again.
On the Independent benches all of the usual suspects rallied round Meryl, with Cllr Stephen James almost bursting with pompous satisfaction at Huw Lewis's volte face. Cllr Gwynne Wooldridge, board member responsible for education, described Meryl Gravell and chief executive Mark James as "the dream team".
If things were not going downhill fast enough, up popped Labour leader Kevin Madge for one last shove. Things had not been easy for the leader, he huffed. "I've done it, we've all done it," he claimed, meaning sayng something "unfortunate" and being quoted in context. Other councils had gone down the pan, but Meryl had shown leadership,...... improvement, things getting better......
As one councillor commented after the meeting, Kevin Madge's biggest problem is not making the occasional gaffe; it is speaking, pure and simple.
Time was running out, and the chair announced that he would allow four more speakers and then close the debate. We then had three more speakers, and when Cllr Arthur Davies rose, the chair told him to sit down, thereby demonstrating that we can add basic arithmetic to the chair's other deficiencies.
So came the recorded vote. 36 voted against the motion, and 31 in favour. We know that there were just 3 apologies, so somehow this left 3 councillors unaccounted for.
It will now be up the the voters to do the job which the Independent and Labour councillors failed to do.