Not really, Walmart amounts to about 10-12 cents of every dollar spent in the US on fast-moving consumer goods. In Australia Woolworths and Coles/Wesfarmers account for almost 70 cents. At that level, it's not appealing for anyone to try and take them on!!
except Walmart sells things really really cheaply
Actually, at least at the local Walmart, grocery prices have gone up enough over the last couple of years that there is little difference between Walmart and Giant. Some things are cheaper at Walmart and some at Giant.