The passage means that by having the US conquer Mexico, they are being negatively affected instead of being positively affected Randolph is saying that by taking over Mexico, their will become "poisoned by Mexico", which means Mexico will do something bad and negative towards the US.
This passage can be understood by looking at the words used and the "reasoning" behind why some of the text is said. The phrase "brings him down in turn" and "Mexico will poison us" allows us to infer that Mexico will due something negative towards the US.
