There would not be enough vegetables to sustain everyone, first off, nor would there be enough to last for the time between tomorrow and in a few months when the now large number of farmers collect their first massive harvest, so there would likely be food riots and deaths unless the government took over all food distribution and rationed everything out to people.
What would we do with the hundreds of thousands of live animals? They are domesticated, if they are let free they will become fodder for other preying animals like wolves, potentially increasing their numbers or violent tendencies during subsequent years due to an abundance of nutrition. What would all the farmers do, start farming vegetables? Not all farmers know or want to do that. This also requires much more land, which needs to be prepared, etc. If America suddenly went vegetarian, I would expect them to invade Canada or Mexico for its suitable growing land.
Vegetarian also stands to be defined here. Does this mean no meat derivative products? There are a lot of those in many things, even jello is animal hooves. I would think it would be more likely that people would go vegan instead of vegetarian, to totally cut animal consumption from their lives versus just not eating meat and continuing to raise and use animals. So now the leather industry is affected, amongst all others who use animals for byproducts. No more horse glue, non-artificial paintbrushes, etc.
I am of course interested in how everyone just suddenly becomes a vegetarian, as the method for this could result in a lot of different behaviours. For instance, if it was a government forced policy and people didn’t want to become vegetarians, there would be riots, looting, huge numbers of people leaving the country, maybe even escalating levels of violence depending on how these events were treated. In the same thought, if it were forced on people, there would be resistance groups, underground meat smuggling, and a world of people who don’t like being oppressed.
I think the secondary effects from this happening are quite large as well. People leaving the country for other less dictatorial countries means a lot of quitting people from all areas. People simply needing to become veggie farmers to keep up with the demand would have a similar effect. Perhaps the number of job opportunities would lower unemployment, but I think the massive number of people leaving (if they were allowed to leave, that is) would be substantial enough to cause a bump.
Edit: I just can’t see the entire world doing this. We already deal with starvation issues now when we do eat meat, we’d be dealing with way more if only America went vegetarian, let alone the entire world. Plus it’s a huge deprivation of freedom, and this cannot be ignored, I can’t see how every country would be persuaded to do this…