How did the dwarves respond when Bilbo asked for volunteers to accompany him into the mountain?

The dwarves' response to Bilbo's request for volunteers provides an interesting and rare insight into the nature of dwarves as a species. When Bilbo asks for volunteers to enter the mountain with him, he did not have high hopes that there would be many takers. Most of the dwarves do not offer to enter the mountain with Bilbo; Balin, Fili and Kili have the grace to look uncomfortable, but also do not offer their services.

It is interesting to note that the two youngest of the group and the eldest are the only ones who seem uncomfortable with asking Bilbo to undertake this, the most dangerous task of the journey (confronting a grumpy, fire-breathing dragon) all alone. Perhaps this is Tolkien's way of commenting that youth and the elderly can both have a certain kind of compassion that the age groups in between can sometimes lack. Fili and Kili seem to feel bad about leaving the job to Bilbo, and Balin, the kindly elder of the group, offers to enter the mountain part way with Bilbo because he is fond of him, as shown in the following quote. 

Fili and Kili looked uncomfortable and stood on one leg, but the others made no pretense of offering - except old Balin, the look-out man, who was rather fond of the hobbit. He said he would come inside at least and perhaps a bit of the way too, really to call for help if necessary.

Tolkien comments as the narrator of the story that such is the nature of dwarves--they can be decent folk, but they had hired Bilbo to do a dirty job for them and had no qualms about letting him try to complete it. They are loyal and would try to save him if he got into trouble, like they did when he was caught by the trolls, even though he had just been hired by them and they did not really know him.

Tolkien makes a point of emphasizing the dwarves' love and value of money, pointing out that they intended to pay Bilbo generously if he succeeded. This love of money and gold underscores the quest they are on, which is not only about retrieving their homeland, but about recapturing the gold and treasure that were taken from them.