Ask HN: Leveraging offers against current company

I'm currently employed with a kick ass company that I really love. Unfortunately, I'm paid about $20,000/yr under where I should be. Recently I've had headhunters calling me and one company is very interested in hiring me (the offer is almost 100% in the bag). I actually don't have any desire to leave or move, but I can't pass the money up. Meanwhile, I have a big opportunity looming (my dream job/opportunity--interviewed, been in talks, probably a 50/50 on ever getting an offer at this point).

I have a few questions on how to handle the situations. What worries me is I don't want to be unethical and lead the second company on and use their time and money without intention of going there, but their offer will be in line with where I should be paid right now, and I feel like using that to try to get a big raise at my current gig could work. And if my current says no, I have a backup plan. In addition, this company in Cali (the big dream job opportunity) could get back with me any day now and I'm afraid it would be unfair to either accept a job somewhere else, then leave immediately if the big one comes through, or to get a large raise with my current, then turn around and leave immediately. How should I approach this in the most professional and ethical manner?

note: throw away account