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?
It's hard to say for how long would the fees be high. If users will wait with their transactions and attacker's transactions have the highest fee in mempool, then the attack will be effectively for as long as Bitcoin transaction processing capacity allows it. For one million transactions, that's about one day. But if other users will bump their fees to get their transactions confirmed in the next few blocks, then the high fee levels would last for longer.
The bottom line is, such attack costs a lot of money and it can't stop Bitcoin transactions from being confirmed, and its effects don't last for long.