Seems to me that there is a bit of a disconnect between "not caring too much" and saying no to additional assignments/projects, and being "well-liked by your . . . boss."
If your boss is the one that is giving you additional assignments and projects, how do you say no and not care too much while remaining well-liked?
By saying first thing when you come in, "Good morning Boss! How's it going today?" Maybe ask them how the previous day's round of golf went, or if their wife who was sick the other day is feeling better, or if their kid got that giant homework assignment done (you'll know these things because you will check in with them all the time and ask them how they're doing). That is, show interest in them as a person. Same goes for co-workers. As the relationship progresses, you might even joke with them how you hope you don't have to golf against them some day, or whatever.
Once idle chit-chat is done with the boss (which probably took all of 20-30 seconds), I might tell them the status of that project I'm working on that they care about. Or, tell them something positive that developed, or that Client X was pleased with the demo we gave them, etc. That is, demonstrate to them that I'm doing something of value to them and keeping them informed without them having to ask me about it.
Doing those things, your boss (and co-workers) are going to like you. Your boss is not likely going to dump the crappy work or extra assignments on you, because he likes you. If something bad has to happen like layoffs or salary cuts, you'll be last in line because they like you and value you. If you don't complete the 1000th TPS report, they likely won't even give it a second thought since they probably don't need it anyway. And if they do think about it, they'll figure you're a solid guy/gal and probably figured out on your own that report is pretty useless. If they really do need or insist on that TPS report, they'll tell you and then you'll have to do it, or pitch them on a better way to get the information without the TPS report. They'll listen to you because they like you.
I'm not saying I'd institute a "zero tolerance" policy for being called at home, or that it's okay to be a slacker -- far from it. If they called me at home (sparingly), I'd do my best to be super helpful. If there was truly an emergency (and I mean emergency), I'd handle it as best I could. If it's not an emergency, I'd tell them the action plan and that I'll address it first thing in the morning when I get to work. If they start abusing the privilege of calling me at home and professing emergencies all the time, then it's time to exercise those other options, such as transferring within the company (easily done since others like you so much) or taking a job elsewhere.
My point is that being the friendly, jovial and caring guy/gal at work counts as much or more than doing BS work. A lot of really good workers with their heads down are overlooked because they're quiet and viewed as "asocial" or unfriendly -- i.e., not the kind you could put in front of a client, not a leader, not promotable.