I really like the $2 Attack card idea--I think it would interesting for one or more to exist, just for the variety.
I think you could make certain mechanics work, though they'd probably need to be balanced by adding one of two base benefits (+1 Card, +1 Action, +1 Buy, +$1).
A couple of ideas that might work:
Idea 1: "Each other player with 5 or more cards in hand draws a card then discards 2 cards."
Less damage to your opponent than Urchin, since they get to draw a card before discard, and it doesn't necessarily drop them down to four cards (if you'd played Governor, Council Room, etc.). Cycle has some chance of helping them... Not sure what base buffs to give this version.
Idea 2: +1 Card, +1 Action. Each other player with 4 or more cards in hand draws a card then discards down to 4 cards.
I like this version. It's similar to Urchin, but can't bloom into a mercenary. And spamming it isn't helpful because subsequent plays actually help your opponents. So it's a $2 cantrip Attack that's only effective in low doses. Everyone will likely buy 1, few people would buy more than two unless they were trying to use it as part of a three-pile strategy.
Idea 3: "Each other player gains a Copper, putting it into his hand."
With the right balance of buffs, this might work. Maybe +1 Card, +1 Buy or +1 Card, +$1. You don't want to make it easy to spam.
To prevent spamming, maybe you could have it be: "+2 Cards | If this is the first time you've played $2-Attack this turn, each other player gains a Copper, putting it into his hand."
Or, you could have it be: "+2 Cards | Each player with 5 or less cards gains a Copper, putting it into his hand."
I think this last version is the most interesting, because of how it could synergize with hand-size attacks if you have the extra actions... If you can reduce the person's hand size then hit them with a few of these, to add multiple Coppers to their hands at once.
No matter how you run it, adding a copper per turn to opponent's hands is effective, but because it's in hand, it helps them with early buys, so it's a balancing act, particularly if good trashing is on the board. This is definitely less powerful than something like Ambassador. Some versions of this card would actually be most effective mid/late game when you are trying to dilute a player's deck.