Worry Not, O Mother!
Denise gave some excellent advice.
Both of our kids were the same. Our son was slightly worse than our daughter. My dad had me in tears one time, seeing my son eat only mac and cheese, pasta with plain tomato sauce, chicken hot dogs, and grilled cheese. Always French toast or oatmeal for breakfast. That was his whole repertoire. My dad yelled at me, saying my son would be retarded as his diet didn't give him sufficient nutrition for brain growth. I tried to explain that this was all he'd eat. We went through it all. The battle of the wills, the "You're not leaving the kitchen until you eat every, last bite," which was promptly followed by his regurgitating all over the table. I couldn't sleep at night for fear that my son was going to be retarded, and it was going to be all my fault!
Our son, however, had other plans. He taught himself to read, beginning at 18 months. He'd spell out simple words on his magnetic letter board. I thought his dad did it for him, and his dad thought I did it. My, my. Weren't we surprised to find out the little dude did it all by himself! I never taught him. He managed to "decode" this thing we call the alphabet into words. I have no idea how. But by the time he was 3 years old, he read proficiently enough to read me the morning paper out loud. He was probably the only 3-year-old who grasped the concept and enjoyed discussion of "nuclear proliferation."
When it came time for school, they didn't know what to do with him, as his problem-solving abilities and creativity was more than the educators had ever seen. They ended up skipping kindergarten altogether. By the time he was a 16 year old senior in high school, he was spending 3 out of 5 days at the local State University of New York for his classes. He started college with a year and a half worth of credits already. He scored near-perfect on the SATs (perfect on math, one wrong on verbals) and 5s on all his AP exams. He was a regional chess champ.
So the bottom line is although his diet was UBER-lousy while he was young, it was nothing at all to worry about. All that stressing, all that yelling my dad did, ("Why don't you ever feed that kid something? He's gonna grow up retarded!") was for naught, except to make me doubt my maternal abilities. My son is living proof that your 2-year-old will grow up just fine.
BTW, the post script is that although he was Biafra-type skinny while a young child (ribs showed through his back! It was really embarrassing!) he discovered that food can be pretty darned good stuff. He's actually husky now, and eats almost ANYTHING that isn't nailed down!