No, the reason Democrats take shots at Ayn Rand is because Democrats have the moral high ground in the public's view, and have for decades, and there has only been a single person to challenge that: Ayn Rand. She really is a threat. If the Democrats lose the moral high ground, it's over for them.

Contrast this with Republicans: They are generally quibbling compromisers who say they are opposed to government expansion, but actually agree with it on a moral level, so all they accomplish is barely slowing down the rate of government expansion. The Bush presidency is a case in point, but you can see this "quibbling compromise" in practically all major Republican politicians.