I am just finishing my first year as a physics and math major
I got a work study job with my physics dept, (not really undergrad research) but, I do get to meet and know all the faculty, I help them with petty stuff like fixing computers, but also with setting up labs, and doing small experiments, I also get to go to all the colloquium seminars, and I get paid. Its really a wonderful opportunity.
Our dept has a year long research project for all freshmen to do as well, its a group project where you pick your own topic, do research in the theory, and then do experimental test to see if its correct. My group studied Amplitude modulation, specifically Modulating a Laser to transmit an Audio Signal.
I also, through connection from a friend, Have an internship at UMSL (my hometown) this summer in their Physical Chem dept. doing research in Intracavity Laser Spectroscopy (although I am not sure what I will be doing exactly, it could very well just be crunching numbers or filing papers)
So in short (well long rather) It is possible, but ti takes your willingness as well as just connections. Talk to all your faculty, see what they are doing, see if they need help, ask if they know anyone who could use help, just make it known that you want to do it and will put forth the effort. If you are alzy, never come to class, and slack off, they won't hire you, so show them that you want to do research and will be willing to help out