My wife suffers from Vash-itis (easy, fellas): the inability to say
no to interesting projects or "important" work.
Saying no is an art form, making "no" stick a skill - say no with a solution: "I'm buried but here is what I would do: contract the work out, assign to the work to someone else, assign work I am currently doing to someone else, or wait until I am free, etc.
Also, never allow their poor planning to become your problem...take a day or two to respond so you can formulate a solution. Use a straw man: My wife is sick so I need a day or two. My dog ate my homework, etc...
However, also say yes with a solution: "I'm in but you need to talk to Bubba about taking me off the Bridge over the River Kwai project before I can commit, he is counting on me. Make it their problem.
Hasn't worked with my wife, I suspect your are domed [sic] as well