Take job w/ lower salary?

Had an AWESOME interview for an AWESOME opportunity. We meet Tuesday to review the offer they have prepared. I did my homework on what my value is worth for my skills / experience, and shared that with them. I am preparing myself for what to do if they come in too low, because they’ve said several things that hint they will. In my current job I am underpaid. I learned this from the market research. Therefore to accept a job for less pay would be getting even further behind market. I don’t want that for myself. Shouldn’t it be possible to find an AWESOME opportunity that also pays more? Or is that not accepting the 50% of everything sucks mentality? Thanks!