Combating The Nimzo Indian and the Budapest Gambit

So, I've been playing a lot of blitz lately as a way to sure up my repertoire. I've actually been quite satified with most of my opening selections against the entirety of my opponents attacks. The only two I've had a bit of a struggle against is the Nimzo-Indian and the Budapest Gambit. I've decided to play a3 against the Nimzo because I just saw a great article about it on this site. Is that the right idea? Additionally, I always find myself on the recieving end of a budapest thumping. Any suggestions for a line in the Queen's Gambit to stuff the budapest?

Ajedrecito, I think he meant the Saemisch, 4.a3 Bxc3+ 5.bxc3. Personally I think it leads to pretty messy positions that I find hard to understand. 4.Qc2 isn't easy to handle either, you avoid the weaknesses but black gets a lead in development. So I prefer just to play the 4.e3 (Rubinstein) main lines, I think they lead to more typical 1.d4 play.

Against the Budapest, I like 4.Bf4 (prevents it being shut in).

Thanks! 
As far as the "Alekhine Attack" against the budapest? Any thoughts? 

Interesting, You think I could get away with it on a Class B-C level? I mean, it doesn't make too much sense to play a line that won't work to my favor when there are lines that do. But, I think it looks interesting enough. 

Thanks for that cool line Pellik! 

@pellik Yes, this is the line that ajedresito wrote about.

Kramnik v Svidler 1992 used 4.e3 against the Budapest, and is quite instructive. I also read somewhere that Kasparov played 4.e3 against it in a simul, but don't have a link to the game.

That was a good example. I especially like the very violent pawn pushing. That fits my style quite well.

Keep in mind that Svidler just won the World Cup. He's no pushover.

But that game makes him look like an A player.