I'm a brit, and I have a very high tolerance to broken English, however I'm from the north where Scottish/Welsh/Irish and various non-English-speaking minorities are much more prevalent and where people generally take more time with people.

I wouldn't say Americans are more tolerant in general, however I suspect they are in the California area. I've met a lot of Americans who are very intolerant of broken accents, the same seems to go in Canada too (where I currently live). People in the Greater Toronto Area can be much more intolerant of accents, where as people from the Atlantic and Prairies seem much more tolerant.

I don't know what causes this intolerance, however I believe it may be caused by a lack of exposure to different accents. I tolerate accents very well and tend to have a chameleon-like ability when it comes to moving between areas. However, I regularly visited France growing up, I had Scottish + Welsh + Irish teachers throughout high school and have visited lots of European countries, so I wonder if it's simply due to lack of exposure.