Bitcoin has a fee market, so you can't pay a fixed price to effectively stop legitimate transactions from being confirmed. You can make a million transactions with $1 fee and it won't mean you have bought all transaction space for a day - it would mean that the users who have paid $1 or less will have lower chance of getting their tx confirmed and will suffer some delays, but those who paid higher fees won't be affected. Essentially, trying to DDOS Bitcoin can only increase the transaction costs, not actually deny service, though for some cases, like micropayments that would become uneconomical, that would be a denial of service.
So now my question is, what would be the impact of a group of people sending 1,000,000 transactions at $10 ? It will just piss some people off because fees would jump from $1.5 to $10 ? and it would be absorbed in only a few hours?