Solid churches develop tithers instead of raising money. I would not be surprised if the day comes when many churches may not have budgets at all and if they do, they will track human assests as much as financial. They develop tithers who give out of gratitude rather than to meet a budget. They encourage their people to raise their own money for non-core ministries except for possible seed money or in the case of starting a ministry that is intended to be a core ministry from the start as in the case of a new worship service. They see stewardship as a lifestyle, spiritual issue instead of an institutional, business issue.
Common sense has to prevail.
If a church feels what the small group is about is crucial to the future of the church, the best thing to do is give them seed money. If not, the best thing to do is let them take responsibility for raising the money. This does not apply to core ministries. The mission statement. In such a system there can not be any dollar amounts.