Rosie was hurt. She was BEGGING Elisabeth to just come out and admit that what the Fox people (that EH defends to hell and back as being "fair and balanced") were misrepresenting her views.
If you reduce it to high school friendship level, basically what happened is Elisabeth is stuck on being accepted by the "cool group" (Hannity et al), which spend a good amount of their time making fun of and lying about Elisabeth's friend Rosie. Rosie finally gets fed up enough to want ask for the record if Elisabeth agrees with the people who are saying unfair things about her. Elisabeth then says "You're on your own - don't drag me into this."
When your friend is hanging out with the people spreading lies about you... and then won't contradict their lies... what do you do?
Elisabeth wants to have it both ways -- decorate cupcakes and giggle about the kids with Rosie on The View, and go on FoxNews and suck up to the same people who are savaging her. A simple "We disagree on politics and I think she's 100% wrong on most issues, but Rosie's a great person and my friend" would have been fine. The problem is... Fox only needed Elisabeth because it was a way to get to Rosie. So that was not acceptable to them, and she knew it. If she wants to play at their house, the price is stabbing a friend in the back. The fact that it was so easy for her says all you need to know about her character.