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I think poor people have no shot at getting to heaven (assuming heaven is a tough place to get into). Poor people have everything to gain by being Christ-like. Rich people don't. If a rich person gives up his own happiness and fulfillness by selling all that he owns to help the poor, he is doing by far more than a poor person could. Therefore, only a rich person has a shot of getting into heaven.

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I think there is a good chance this was not very serious, but anyway...

Luke 21
The Widow's Offering
1As he looked up, Jesus saw the rich putting their gifts into the temple treasury. 2He also saw a poor widow put in two very small copper coins.[a] 3"I tell you the truth," he said, "this poor widow has put in more than all the others. 4All these people gave their gifts out of their wealth; but she out of her poverty put in all she had to live on."