You might want to start looking for a mentor before you get too deeply involved in developing your project. It's great to have some broad ideas, but it isn't a good idea to box yourself in so far that your project isn't a good fit for those on the faculty who might be interested in mentoring you over the summer. Also, potential mentors might have some ideas for projects that would be a good fit for both you and the mentor.

Before you start approaching potential mentors, be sure to check with your McNair program to find out what the program expects of the mentor (for example, the mentor might be expected to write a brief biweekly status report commenting on your progress, as well as validating that you have met milestones for your project). You might want to develop your project proposal with your mentor and to start working together on a realistic set of milestones. The McNair program here tied a large chunk of the summer stipend to meeting milestones.

Have there been other McNair scholars in math at your school in previous years? You might check with your school's McNair program, your department head, and/or your coursework advisor about this. If there have been others, you might also get some tips about potential mentors. You might also check with your coursework advisor or your department head about which faculty members have mentored undergraduate research students. Did you submit letters of recommendation as part of your application? If so, you might want to share your good news with your letter writers and ask their advice concerning potential mentors.

Please don't worry about finding a big result. This is an opportunity to get a taste of research and to learn about some new topics. You will probably be expected to write up what you learned at the end of the summer and present at a conference for McNair scholars. Good luck!