The proposed committee structure, to be debated by up to 1,000 delegates at the meeting in central London next Tuesday, has metropolitan, district and unitary representatives on the policy and strategy committee being elected through regional bodies, while the counties have chosen to have their 13 representatives selected from a separate county body.
It had been agreed the counties could have their own group to calm fears that their voice would be swamped.
But in recent weeks, Shropshire CC has led moves for counties to participate in the regional bodies. It proposed a motion to next week's assembly to bring this about, but withdrew it because the support promised from 12 other counties was insufficient to overturn the existing plan.
The highlight of the assembly will be a keynote speech by Labour leader Tony Blair.