The meat industry is indeed a major contributor to global warming, and other environmental effects such as deforestation.
However, it does not seem that stopping eating meat by itself is enough to stop global warming.
In Diet, Energy, and Global Warming by Gidon Eshel and Pamela A. Martin, the authors claim that moving from meat-based diet to a vegetarian diet saves about 6% of the greenhouse gas emissions:
We examine the greenhouse gas emissions associated with plant- and animal-based diets, considering both direct and indirect emissions (i.e., CO2 emissions due to fossil fuel combustion, and methane and nitrous oxide CO2-equivalent emissions due to animal-based food production). We conclude that a person consuming a mixed diet with the mean American caloric content and composition causes the emissions of 1485 kg CO2-equivalent above the emissions associated with consuming the same number of calories, but from plant sources. Far from trivial, nationally this difference amounts to over 6% of the total U.S. greenhouse gas emissions. We conclude by briefly addressing the public health safety of plant-based diets, and find no evidence for adverse effects.
Note that this study is based on US data - the effect would be smaller in places where current diet already includes less meat.
I don't know what level of CO2 emission reduction is needed to stop global warming. but the change of green house gas concentration between the beginning of the industrial revolution and today is about 40% (data from US Department of Energy) - much more than what will be saved from stopping the meat industry. This is a lot, but it doesn't appear enough.
Based on Target atmospheric CO2: Where should humanity aim?
A level of 350 PPM of CO2 is desired to stop global warming, while the current level is 385 PPM - a difference of about 8%.
This is much closer to the amount reached by the Diet, Energy, and Global Warming paper, but a similar study that takes into account global (and not just US) data is needed to get a real conclusion.