If you eat breakfast cereal with milk in the morning and a sandwich made from commercially-sold bread and meat for lunch I suspect you would have to try very hard to develop any micronutrient deficiency.
I didn't research it for more than five minutes, but I suspect someone on such a diet could easily develop a vitamin K deficiency. The DRI for males/females is 120/90 mcg/day, and I found no breakfast cereal, milk or bread that had anything close to that. There are too many lunchmeats to check, but the highest values I saw were in the 3 mcg / 28 oz range.
This source indicates that vitamin k uptake is very poorly understood, but that vitamin k deficiency is rare in practice and that you have to put people on a very low vitamin k diet for an extended period to show any negative effect at all. This would be very weird except that our gut flora is known to produce vitamin k, so we're probably producing a fair chunk of what we need internally.
From that article:
...It is commonly held that animals and humans obtain a significant fraction of their vitamin K requirement from direct absorption of menaquinones produce