Basically I remember when my daughter would be happily playing. Then I'd try to leave the room and... yeahIthinkNO. The emotions expressed ranged from "No" to "HOW DARE YOU SIR!"
Remember that below 2 years, their emotions are very immediate, there's no "It's just 5 minutes", they're unhappy now. Because of this, the gap between "Worst thing ever" and "Oh so awesome" is pretty quick.
Firstly, remember that when you leave him with other people it's as much for your benefit as his. A bit of self-care is a good thing, especially when the alternative is frustration at his own complete self-centred nature (You're tired? BABY CARES NOT). If you need a break, just take the break and relax. He's perfectly safe, it's just he wants you to do something else, and negotiation is for older children.
Secondly, this will get better. You have to remember that he's been basically in constant contact with about 3-5 people his entire life. All of you out of the room is a big shift, and it takes time to deal with. However, even as it gets better, he may not let you know. Our 15-month daughter still rages like a hellhound as long as we might be able to hear her. What we've found is that when we've left, she settles down, especially if someone's making an effort to entertain her (We've found the gap between "HOW DARE... Oh they've gone, okay let's play" is about 2-3 minutes). Confirmation that he's settled from people via phone is important for your piece of mind, make sure to ask for it. It costs them nothing, and really makes you feel better.
Thirdly, how you leave is important. It's always tempting to fuss, and you certainly don't want him unaware that you're going, but once you've committed to the bye, don't look back or try to calm him down, as it just makes your leaving a bigger deal. Very often, the fact that you're feeling guilty/upset about it (which is perfectly normal) is what's upsetting him, and as you can't fake being okay with leaving, just leave him with the happy people and go sob on the bus. If you ever want someone else to be looking after him, suck it up, wave bye-bye, possibly a peck on the cheek, walk out, and let your boy inform you of the unacceptability of this decision. Then stop at the corner to mope a bit.
Finally, it sounds like you're worried that he'll develop insecurities if you leave. While this is true at a very young age, and might be if he's already a bit insecure and not being given enough attention (e.g. very large nursery/daycare classes), nothing you are doing will make him a basket case. As long as you do come back, he'll get used the fact that you will come back. He may still be against you leaving, but that's a nice problem to have.