A friend of mine works cleaning houses. She gets up at 6:00 in the morning and works all day.
On top of this, she finds time to go out witnessing, teach Sunday School, and organize youth activities.
On top of this, her sister came to live with them and brought her children, which my friend now takes care of for most of the time she's at home from work.
On top of this, she is constantly thinking of ways to dig into the Word of God (we had an hour-long Skype conversation yesterday to pray and talk about what we had read in the Bible that day).
In the midst of this workload, she memorizes somewhere from 2 to 10 verses a day.
Given her passion, dedication, and determination to find a way to do what God wants her to do, let me not say "I have no time to work for God."