About Gigs
Gigs are not one off jobs, they are things you do for a living. So just cause a guy hires you and your boys to deliver these trucks full of scrap metal to the guy on the other side of the bandit ridden wastes--doesn't mean now you're a transporter. You might be, if people know this is what you do and you got guys coming all the time to ask. But if it's a one time thing, it's not something you're juggling off-screen.
Your Answer
Juggling is really about how many jobs you aren't doing. Not how many you are doing. If you have too many things you're trying to do, but can't well, that's like having every weakness on your hard-hold. There wont be enough time in a session to have forty things going wrong all the time without literally consuming every moment of game time. That's why you've a limited number of things that are weaknesses, and you push one on a partial or the few on a miss.
For the Operator, they have a +2 juggling and start with 4 gigs. So they're always leaving two of them off the table, but can choose to leave more. If they only work one, then on a partial, that one works and nothing goes wrong. This is playing it safe.
To make things interesting, the obligation gig is risky to ignore. (otherwise it would be a rather dry and mechanical, pick your jobs see if you get paid or what). So the Operator is choosing between two paying jobs and some risk, or keeping the obligation gig out of the picture for less possible reward. This choice is important to the character, its The Challenge.
Now lets say your operator is Easy on the Eyes and has a thing for the Ladies. So he's sleeping around, with like five different women. Of course none of them know about the other ones and at least two of them are wed to some pretty scary dudes. But that's just the Operator's thing, juggling. To make this even more tense is the fact that each one of them is now a gig in and of themselves.
5 girls, means five different obligation gigs, means +5 juggling. Now this does mean that the Operator has a +7 juggling. Sure. but what two things is he not going to try to work, and how will that impact the game. If he is money starved... does he risk letting his eyes off one of the girls while he goes and cleans something up? What if he hits a partial? What gig went WAY WRONG. Did a girl figure him out, is she bring some "hell hath no fury" to the table? What did she learn, how did that blow up. Is the gig DONE because he fucked up bad? Or is she fucking pissed, knows he is cheating and STILL want him for herself? ... what if he is working all the women, and rolls a miss... and all of the go belly up? What could that do to him, how many husbands might be coming at him? How many might be hurting the women, what the girls doing to each other, what are they doing to him? The answer is they're probably all doing something different--but in a climatic failure like that, most if not all those gigs will be resolved here.
The only way for them to remain is actually if they fall into a new pattern of tension that can co-exist. Since the girls know he was cheating on him, and probably know each other, and the gigs are still around so they're still seeing him... Well, there must be tension. Maybe they're ground rules, made they're working together, maybe his life just got turned upside down. Maybe he had to make concessions to them, or maybe he's working to keep their wrath at bay.
See if the juggling didn't increase, or got limited somehow, all of a sudden there would just be too many things going on during the session. Total failures being the exception here, because most of them are final. Some gigs are like "protect this person" and a failure means that person is dead. That's pretty final. Most obligation gigs work this way, if they trigger, the shits hit the fan.
Clarification
Every obligation gig, or normal gigs gained through experience, adds one juggling.
Every obligation gig that's resolved forever removes one. (except the advance)
The reason this is allowed to happen, is hitting a 10+ can only be as +3. So partials are very likely. The more you work, the more might go wrong. You hit that miss though and you were working 13 jobs? lol.... You've probably got every gang, every powerful figure, every mad husband in the world coming after your ass and ending you. It'll be messy and very little will be there when you come up for air, excepting your skills at those things mind you. Time to start up somewhere else, or hold that thing you do ransom until someone decides to give you another go.
Response to Daniel
I'd go as far to say that you can always earn more obligation gigs, as clearly shown in the operators special. Resolving them can happen during game play. The advance is letting you resolve one of them DESPITE game play. Obviously you dont want to go too crazy here, you and the player are juggling these things too. Dont overwhelm yourselves.