I think that some time has passed since Ariel saved Eric and "Under the sea", though it's clear that the deal was in the same day of "Under the sea".

Hard to tell underwater but I'm pretty sure that it wasn't that much of a time lapse.

I always thought so...

I think that, at least 1 or 2 days have passed.

I always though Sebastian sang "Under the Sea" and Ariel made a deal with Ursula on the next day, after Ariel sang "Part of Your World Reprise".

that's what i thought but i haven't seen this movie in about six months so...

Not really. After the Part of Your World Reprise and before Under the Sea, Ariel's sisters call her out of her room, shouting "You've been in there all morning!" Then she comes out humming, puts a flower in her dad's hair, then her sisters reveal to him that Ariel's in love, then the next scene is Sebastian fretting before "Under the Sea." This implies it's been AT LEAST a day since she rescued him.

However, when Ariel goes on land, the house keeper says to Eric, "That's the first time I've seen you smile in weeks." I don't know, I always felt it implied that he'd been upset because he spent that time looking for "that voice," but it's possible that's not the case.

Either way, it's at least a day between "Part of Your World (Reprise)" and "Under the Sea." Possibly a couple of days, MAYBE a couple of weeks.