Below, I work through my thoughts and understanding of scriptures I feel are used out of context. The format is loosely the passage reference, the context the passage is used in, and what I think the correct context is.
Hebrews 11 - the entire chapter
This passage was used to challenge and inspire disciples to evangelize. In the context of the message, the plea went something like this: See the great things that God can do through you if you have great faith. Rather than reproduce the entire chapter here I'll let you read it on your own. I would guess that many preachers use Hebrews 11 to support the premise of the great things God can do through a person. I would not argue with that premise as I believe it's true. I've seen these things working in my own life. The context of Hebrews chapters 10 and 12 are generally ignored, though, when the stories of Hebrews 11 are included in a message. For me, the context of Hebrews is that the audience is facing some tremendous challenges, even to the point of death, and they are backing off on their faith and the message of Christ. Hebrews 10 sets this context and explains to the audience that they, themselves, faced similar challenges earlier in their Christian walk and overcame them. Then Hebrews 11 shows the audience that in the face of tremendous trials, a number of regular human beings just like them also stood firm in their faith. The lesson is that God delivered them. Hebrews 12 encourages the audience validating that the folks highlighted in Hebrews 11 and a host of others are watching them and cheering for them, and that God is strengthening them so they will overcome the challenge. Faith, as I read it in Hebrews, is a continuum, like body building, where an individual starts working out their faith and growing stronger the more their faith is exercised. This is different than the one-time application of faith that I'm used to hearing when Hebrews 11 is used from the pulpit.
2 Corinthians 8:1-10
This passage was used to support a position for increasing giving to the local church in order to meet the budget needs.
Now, brethren, we wish to make known to you the grace of God which has been given in the churches of Macedonia, that in a great ordeal of affliction their abundance of joy and their deep poverty overflowed in the wealth of their liberality. For I testify that according to their ability, and beyond their ability, they gave of their own accord, begging us with much urging for the favor of participation in the support of the saints, and this, not as we had expected, but they first gave themselves to the Lord and to us by the will of God. So we urged Titus that as he had previously made a beginning, so he would also complete in you this gracious work as well. But just as you abound in everything, in faith and utterance and knowledge and in all earnestness and in the love we inspired in you, see that you abound in this gracious work also. I am not speaking this as a command, but as proving through the earnestness of others the sincerity of your love also. For you know the grace of our Lord Jesus Christ, that though He was rich, yet for your sake He became poor, so that you through His poverty might become rich. I give my opinion in this matter, for this is to your advantage, who were the first to begin a year ago not only to do this, but also to desire to do it.
While the passage does a fantastic job challenging the heart of the giver, and someone with a giving heart might do well to evaluate if there is more he or she could do, the passage itself has nothing to do with local church budgets. One might even argue that the local church, in light of this passage, should give up some of its own programs in order to imitate the behavior of the Macedonians. The church in Jerusalem faced a severe regional famine. To help those struggling to survive, the Macedonian and other churches pooled their resources to help them. The plea for support was to meet the basic survival needs rather than pay the salary of a new staff member or cover the cost of higher health insurance premiums. I think a better analogy for the use of this passage might be asking the local church to give sacrificially so that the money could be used to support a church in, say, sub-Saharan Africa where the shoeless members walk 5 miles on a Sunday morning to meet under a tree in a field to worship. Perhaps the money could be used to buy shoes or build a rudimentary structure to protect worshipers from the elements.