Yes, Willow, you got it right. The legislature has the ultimate law-making power (mmm.... mostly, let's forget executive orders for the moment). With the consent of the executive, a simple majority is fine. Without the consent of the executive (i.e. veto), you need a super majority.
Side note: The pocket veto: Congress gets a bill to the president, and there is a certain amount of time he has to sign it or veto it. If there is less time until the end of the Congressional session that the time provided for signing, the President may simply do nothing, and let the legislative session end without the bill being passed one way or another. This effectively kills it until next session, and is known as the pocket veto.
Unfortunately, I can't help you with the EU. Ramonster?
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