There's a thought that cursing attacks really kill engines. This is probably because curses, in general, and like so many other stop cards, actually do hurt most engines rather badly. They stop your different components, needed to draw, from coming together. And all this in a way that isn't as harmful to money, which just misses a little bit of density.
But in actuality, there are a large number of situations wherein engines can reign supreme anyway. Because curses usually do screw you up very badly, you want a way to keep your deck very clean. Generally this means some form of trashing. And because you need to actually connect that trashing with the curses, not just any trashing will do. Generally, in order to maintain your clean deck and thus running engine, you need to be drawing large parts of your deck before you get hit with too many curses. It's generally quite important to get ahead of things and be reactive rather than proactive. There are a couple ways of doing this. One of the ways you can do this is to have strong trashing and get thinned out quickly. Another is to get your engine up and running and strong quickly. Occasionally, there are other ways of getting around things, such as when your can draw even through so many curses (say scrying pool) or when you can engineer massively massive trashing somehow (say with forge and some way to get at least one big hand, like with tactician - the trashing equivalent of a mega-turn). But in general, you want to have a strong enough trasher to get things down, with a good enough engine to play it often enough to do so, too.
Exactly how much time you have is a function of a few different parameters. There is a question of what you can do with your engine once it is up and running. The stronger your engine is - this could mean more points available, it could mean stronger attacks, more buying power, could mean a lot of things - the more time you have. Probably the biggest thing, though, is how long the game is going to last. The opponent of the engine player is looking to score enough points and most importantly to get the game over. In the long run, the engine is going to be better. The big question is whether the game will be long enough for that to come through. So money strong enough to run down 50% of the points (or close enough to that amount) or to grab all the provinces (this is highly unlikely) will be a problem. But generally, the bigger issue is a three pile ending. Curses are going to run, almost always. A second pile to likely run, which is something the engine often wants, can make a lot of problems, as the money player can then target down something, usually duchies, to be a third pile, ending the game before the engine player has time to get going. This is the biggest wepon that the non-engine player usually has in such games.
Example games:
http://councilroom.com/game?game_id=game-20130106-105232-6f7c7712.htmlIn this one, I use lookout for the trashing and scrying pool for the draw. This stops me from getting rid of all the curses, but the draw is so powerful, and with grand market and peddler, even the lack of villages isn't too much of a problem.
http://councilroom.com/game?game_id=game-20130108-185736-a16383ff.htmlApothecary provides a nice engine base, complemented well by worker's villages and an eventual margrave and alchemist, with nothing more than remodels for trashing, but this is enough to overcome mountebank.
http://councilroom.com/game?game_id=game-20121226-082756-3f5af445.htmlWalled Village, Embassy, oracles, and a witch are enough draw here with Forge on the job.
http://councilroom.com/game?game_id=game-20130111-215827-2deafe44.htmlHere, IGG with coppersmith support can run decent hands all day long, but remake and upgrade deal with curses, and scrying pool to draw everything, and the province train is coming.
http://councilroom.com/game?game_id=game-20130119-150121-7e5ffc9e.htmlHere my opponent goes for IGGs once again, and gardens certainly go well. But he makes the mistake of not having the three piles in sight, and abandons draining the IGGs down too early, which leaves him unable to end it. Moreover, Steward gives strong trashing and engine component down the road, with Bazaar as an excellent village.
http://councilroom.com/game?game_id=game-20130128-142736-ca25e0f5.htmlHere, an early trading post and later upgrades combine with scrying pool's excellent draw and a massive conspirator engine to win the day over sea hag and a late mountebank.
http://councilroom.com/game?game_id=game-20130130-135139-d8614927.htmlHere, a double-tac deck with trading post, with militia, shanty town, and oracle helping along is able to eventually get through the flood of IGGs and make a pretty good bid at comeback, but my opponent puts his head down and goes on a mission to pile out IGG, curse, and silk road and is acle to come away with it. A classic close game which can go either way - nice clashing styles.
http://councilroom.com/game?game_id=game-20130203-091410-94ee9233.htmlGoons gives massive point potential, throne room, worker's village, nobles, torturer, and minion all provide potential to get those goons in play, and forge can clean up. This is able to overcome even mountebank. The key points here are forge, which we both need, and my esteemed opponent turning for points too early, which gives his engine the opportunity to break, which it does - fortunate for me, because it took a long time to set this engine up. If he is able to keep enough lead with the deck relatively thin, he can look to three-pile on me pretty safely.
http://councilroom.com/game?game_id=game-20130131-155828-6f6a72e3.htmlIn this one, there's a sea hag slog, but I'm eventually able to use native village and forge to get an enormous trashing, and then I have a roaring engine. Unfortunately, in the process, most of my deck ends up on the mat, which really slows me down in getting to forge. But when I do, I come neck and neck and would have had very good chances of winning had I played better - probably I needed to be a bit more province-shy.
http://dominion.isotropic.org/gamelog/201302/12/game-20130212-122608-871d4433.htmlBishop is eventually able to cut through all my problems from young witch AND provide my points in large quantity which also don't bring endgame closer. This was very slow, but the later bishop plays don't benefit him AS much, and his fool's golds eventually have hard times finding each other, whereas my hunting parties and shanty towns strengthen and strengthen. Importantly, peddler is a huge huge boon here.