Aidan Millow raised some important concerns. Another is that this card stacks with itself, which could lead to terrible slowing of the game. This is especially bad in a multiplayer game, where there could easily be four of these cards in play consistently. Not every kingdom is capable of overcoming such steep cost increases in a timely (and enjoyable!) manner.
I've spent a lot of time trying to come up with an idea to make a cost increaser work, but it is tricky.
edit: I just had an idea that may address these concerns, although it inverts the card a bit.
Roadblock
$4 Action-Duration
Now and at the start of your next turn: +$2
While this card is in play, -$1 when you buy a card, to a minimum of $0.
Rather than ramping up the cost of the first card, this effectively ramps up the cost of any subsequent cards. The effect is cleaner with the wording borrowed from Poor House, and it does not excessively stall the game since you can still buy one reasonably priced card even when lots of these are consistently in play. Now, I'm not saying that the card as written is good, but I think this mechanism is at least a starting point.