I believe that's an over-simplification (for lack of better words) of the text. If we take that literally, breathing, thinking, walking, talking, every single function is a work. And what Jesus is requiring would be impractical because if we aren't "working" we are decomposing/dead. Only dead people don't work.
The work Jesus is refering to is this: Ephesians 2:8-9, "For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— 9 not by works, so that no one can boast."
Works here in the greek is: ergon, a nueter noun, which (according to the KJV) is translated as work 152x, deed 22x, doing 1x, and labour 1x. It means:
business, employment, that which any one is occupied/that which one undertakes to do, enterprise, undertaking
_____________________________________
Perphaps another explanation is that the work which Jesus is saying doesn't get you into heaven alone is labouring and doing good deed in order to achieve heaven, but the greek work you mentioned simply means to have trust and confidence in. Which is us actually surrendering to Christ which is exactly what we are called to do. It's like falling backwards in Christ arms. Now faith without works is dead though, as it says in James, not that faith needs works but true faith automatically produces work. If you have faith in a chair, you sit on it, if you don't you find another one! But Jesus isn't saying works are excluded, but works don't get you in heaven ALONE. It's like doing and indicative without the imperative. It's not to become a child of God I obey Him, it's because I am a loved, cherished, adored, and precious child of God I do his commandments.
I did a bad job explaining... you bring up a good point though.