God knows all about your situation; nothing that happens to us ever takes Him by surprise. And you should take great comfort in this, because it means He knows what you can and can't do -- including with your finances.
Don't forget, however, that God's work (including your church) does require financial support. Even Jesus' little band of disciples had people who supported them with their money (see Luke 8:3). The Old Testament taught people to give one-tenth (or a "tithe") of their income to God's work, and this is still a worthy standard. The Christians in Macedonia were very poor, and yet "their extreme poverty welled up in rich generosity.... They gave as much as they were able, and even beyond their ability" (2 Corinthians 8:2-3).
Even if you can't give much, I hope you won't stop giving completely. Not only will you have the satisfaction of being part of God's work, but you'll also be a good example to your children. In addition, look for other ways to support your church -- doing volunteer work, for example, or assisting in a class. It can be part of your contribution to your church's work.
Most of all, don't give in to despair, and don't stop looking for work. Commit the future -- and your family -- into Christ's hands, and ask Him to guide you and encourage you during these difficult times. God's promise is for you: "I know the plans I have for you... plans to prosper you and not to harm you, plans to give you hope and a future" (Jeremiah 29:11).