The answer -- it depends upon your age. If you're younger, you'll pay less because the Exchange allows insurers to charge older people more. If you're older, you'll pay more for the same reason.

Now how much more? That depends on the community rating. If the community rating is 2:1 (meaning insurers can charge older adults at most twice as much as young adults), as are in the House and HELP committee bills, older Americans won't pay that much more. If the community rating is 5:1 (meaning insurers can charge older adults as much as five times as much as younger adults), older people will pay a lot more.

It's all about whose pockets from which you're willing to take money in order to make health insurance affordable for the other person.

Yes, Pence WAS schooled.
Just because it wasn't a screaming match or a slam-down, doesn't mean she didn't school him.

Though it's great to see a debate between adults for once, it's still obvious that Pence and his pals are deliberately misleading people as to how the proposed new system would work. And it became immediately obvious to me, when Pence was discussing the issue for small businesses, that he's arguing up a steep hill, as this proposal would likely save many, many small businesses. Health care via private insurance right now is one of the leading causes for small business failure. If the public option takes that burden away from them, then that is an amazingly good thing.
In other countries businesses pay fees to cover health car, the amount more or less depending on the safety of the workplace, air quality, break times etc) - and they pay exponentially - and hugely - less than American businesses do. With a similar model, small businesses will once again have healthy, productive workers, with a far lesser overhead. How that is bad for the economy, only the conspiracy theorist right/RNC would try to explain that as bad or dangerous.
There are many, many more examples of how this public proposal and the surrounding consumer protection legislation would positively affect the economy - but Pence and co, having recognized their death panel/list nonsense is only turning people away from them, are now simply lying about what the new proposal is and how it works. Shultz did a great job schooling him, in an adult manner.

I have heard this argument now several different times, and I don't really understand it. Why would this bill make it more likely for employers to drop health coverage? It adds a penalty for employers that do not cover employees. Wouldn't that make it less likely for them to drop coverage, or am I missing something?

I'm not sure, but I guarantee it'll be better than what's happening now. Companies are dumping health insurance and people are screwed because they can't afford any insurance.

"she didn't really answer the question that I think he was trying to get to"

If that was Pence's real question, isn't it Pence that failed and not W-S?