I must warn you that some may not agree with my answer.
In the first place, the Bible does teach that the worker has the right to be supported by those to whom he ministers:
This does not mean that one is obliged to be supported. It is a right which may be set aside for a higher cause. It is precisely that for Paul, who made it a practice to labor with his own hands (see Acts 20:33-35; 1 Corinthians 9:15-23; 1 Thessalonians 2:8-12). Freeloading was not acceptable (see 2 Thessalonians 3:6-12).
Paul did accept gifts, and when these made it possible for him to devote himself to ministry, he did so (Acts 18:1-5). Paul was not hesitant to solicit gifts for others (1 Corinthians 16:1-9; 2 Corinthians 8 & 9), but was reluctant to solicit gifts for himself personally, even with those inclined to give (see Philippians 4:10-20).
Much of the fund-raising that is done in our country is somewhat suspect, and needs to be carefully thought through. I am supported full-time in my ministry, but have the highest regard for those who have tent-making ministries. Often this is a more effective way to minister, and it relieves the church of financial burdens. There are all to many who would like to pursue full-time ministry and let others pick up the tab (see 1 Timothy 3:3).