When your manager asks you to perform a task and you don't have time to do both that task and everything else you've committed to, tell him that. You can inform him of your workload and still be respectful. Try something like, "Sure boss, I'd love to do X, but I've already committed to do Y and Z, and I don't have time to do all three. Which tasks should I prioritize? Is anyone available to help me?" Then go from there.
If you're concerned about future backlash from not doing a task your manager tells you not to do, follow up your conversation with an email. If there are other stakeholders involved (i.e. people other than your manager request your time), copy them on the email or ask your manager to speak with them. If someone asks you to perform a task and your schedule is full, refer them to your manager. Don't be afraid to use your manager as a buffer between you and the people requesting your time; that's part of their job.
Don't complain about the work ethics of others. It will make you look whiny, and it's irrelevant anyway. The only thing that matters is your workload and whether it exceeds the amount of work you can do. It's the responsibility of your bossmanager to decide how to deal with you having too much work, and it's also his responsibility to deal with slackers. Don't try to do his job.