Is it "just as soon" or "just assume"?

If someone says a phrase that sounds like:

I'd just as soon you don't get in an accident, so I'll call you later.

Are they actually saying "just as soon" or "just assume" or something else?

It's "I'd just as soon" and it means, in expanded form, "I would just as soon have it that [something be true] as that [something else be true]. It is making a comparison between the benefits of something happening one way versus another, and stating a preference regarding the outcome.

Examples:

I'd just as soon eat live cockroaches as go see another movie about vampires.

Here the person is stating a distaste for vampire movies. He would as soon, or as eagerly, eat live cockroaches than watch one.

I'd just as soon you spoke to Bill before telling Marie about this.

Here the person believes Bill needs to know something before Marie finds out about it. There is only an implied comparison here, between telling Bill first and not.

I think Americans screw this up all the time. The examples here make very good sense. "I'd just as soon do X as Y". Perfect. I hear it all the time in a non comparative sense. Drives me bananas. If English weren't my first language it would drive me to distraction.

Ok. Now let's fight about when to use "further" vs "farther" :)

"Just as soon", meaning something very like "I would sooner you don't...", but with the preference left up to the listener. It's a kind of "I can take it or leave it, but, well, leaving it would be easier for me -- still, it's your decision" idea; the speaker's desire is obvious, but not being pressed.

Simply put, "I would just as soon [do one thing] as [do something else]" indicates that there is no preference one way or the other.

"I would sooner [do something] than [do something else]", on the other hand, indicates a preference.

The expression "I would just assume you do/don't do something" makes no sense, nor would the expression "I would just as soon you do/don't do something".