My kitchen faucet is beginning to leak from the connection where it swivels from left to right basin. I've replaced faucets before so I figure this isnt going to best me. So I got a new faucet from my local big box store and set out to replace it this weekend.

However, the existing faucet is secured with a large nut where the supply lines feed through, and three small bolts. I was able to get one out, but the other two are so tight I'm worried they're going to strip if I keep at them. There is also so little room between the back wall of the cabinet and the underside of the basin its difficult to get much leverage. Any tips for an infrequent but not altogether inexperienced DIYer?