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God does speak
This is a very interesting question. Certainly God has spoken to people in the past in very specific ways. To mention a few...
The Source of Subtle Feelings
However, these were never a subtle feeling, but a very direct command of God. That's a very important distinction. A subtle feeling is often attributed to divine guidance when it could be just what someone happens to want. Perhaps some people want to feel like they are in such close communion with God that He is directing every aspect of their lives. However, I do believe this could be true for some people.
Unfortunately, the only way to discern whether or not what someone claims is divine guidance is actually from God is to wait for the outcome. If the waters part, the manna falls from heaven, water comes forth from the rock, walls fall, or peril is escaped, then it's probably from God. However, sometimes there is no visible distinction in the outcome. That doesn't mean there isn't one. Perhaps God really is active in the situation.
However, never in Scripture does God command someone to do something that ultimately results in failure.
Responsibility
Perhaps the issue comes down to where the subtle feelings are directed. If someone has a feeling and decides to do things in their own life accordingly, then they are ultimately responsible for those decisions. It seems, though, that some people can make very poor decisions, all the while proclaiming they are following God's guidance, when they are only doing what they want to do. The problem with this is that the feeling cannot be questioned, no matter how ridiculous, illogical, unwise, or even ungodly it is. When a situation turns out really poorly, people sometimes attribute it to God wanting them to go through that. However, that ends up meaning that God directs people to make unwise decisions, so that it may be better to reject the guidance of God at times--for your own good.
However, if someone comes to you and tells you that they feel God is telling them that YOU should do something, that can be problematic. If it is to stop sinning, then that's probably fine. If it's to make a seemingly foolish decision, I would encourage the person to pray that God would direct them personally rather than relying on the uncertain feelings of another.
Conclusion
Each of us is ultimately responsible for his own decisions, so we have to make the wisest decisions we can and then own them. God can certainly lead people to do things, and we should certainly be open to His leading. Yet, we should not use "divine guidance" as an excuse to fulfill our own desires or wishes. If we say God is leading us, then we should be very certain that it is God and not our own desires or even wisdom.
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Dave Mortons Comment here is supplemental to this question:
How can we apply relying on Jesus in situations where it appears we have to rely on ourselves?
I don't think there's a huge distinction. Paul gives us some instruction in 1 Corinthians 7:17-21, that we should remain in the way we were when we were called, but if a slave can gain freedom, then he should. Obviously there's tons of freedom here to make decisions using our brains, and make the best life we can, always realizing that it's God's decision in the end whether or not he'll bless us. There's enough overspiritualization within the church today, that I don't think I need to add to it. Love God, avoid sin, love others, and do what you're good at. Read Ecclesiastes for more.