Old thread, but I've been trying to nail this for a while too, and just finally got really darn close today, somewhat by accident.
Most of it comes from the bass, and not from pedals, but there are some involved.
First, I'm a playing a Warwick $$ 5-string with rounds. I put both humbucker's in single coil split mode, and had them both at full volume. On my bass this produces a very growly, slightly out of phase Jazz bass-esque tone. I had my bass in passive mode with the EQ flat as well.
I also had a mute by the bridge that I cut from a kitchen sponge and shoved under the strings. With a bit of a smily face EQ on the amp (my bass is super mid-heavy so YMMV) and the proper right hand technique I was 85-90% of the way there.
I also had on my Jacques Fat Burner compressor. This compressor is never subtle, but I had it on one of the less dramatic settings, Sustain around 9 o'clock and Muscle around 2 o'clock. I usually have the Muscle set lower witch I think slows the attack and creates a bit more of a spike before the compressor comes down, but to my surprise the smoother setting worked better.
Finally, the part that was most by accident is that I had on a chorus pedal I'm borrowing from a friend; a Boss CEB-3. The setting was how he left it, very subtle: E.Level 9 o'clock, Lo-filter 10 o'clock, Rate 10 o'clock, Depth dimmed.
The chorus had a very subtle effect, and in a live setting I'm curious how much of a difference it would make, but in a quiet room it was a little extra icing that added that... "je ne sais quoi".
In summation, you can probably get most of the way there with the right bass, amp/eq, and technique, but I found compression and lite-chorus put me that much closer.