Megan and Kyle Williams told the BBC their baby arrived seven-and-a-half weeks early last year, and needed an emergency caesarean.
Mr Williams said for them, the closest service is an hour away.
"What about in peak traffic? What if it all goes wrong and you have an hour, possibly more, stuck in traffic?" he said.
Adam Dance, Yeovil MP, said: "It's absolutely amazing to have this many people turn up and hearing the stories.
"I got into politics to fight for people and make our community better. This is not making our community better.
"The leadership need to really wake up. The time is a huge important factor.
"Trying to send people to Musgrove is going to be an absolute disaster. We need to get this unit open as soon as we can."
Mr Lewis added: "There are clearly challenges with getting the right people in place and the right capacity in place so it's difficult to absolutely guarantee six months to the day, but that's what we're working on."