People usually have a pretty high opinion of their own talents and overestimate their control over events. As a result, you might expect them to overestimate their chance of upward mobility and underestimate their chances of downward mobility. There have been a few survey questions about the chance of getting rich (see my recent paper in Comparative Sociology for more discussion of them), but I know of only one on the chance of becoming poor. This appeared in an ABC News/Washington Post survey in 1990. The question was How likely is it that you will ever be poor: Very likely, fairly likely, not too likely or not likely at all?" 12% said "very likely," 12% said "fairly likely," 34% said "not very likely," and 36% said "not at all likely." 5% volunteered that they were poor now. The survey did not ask them how they defined poor, but a couple of years latr the General Social Survey asked people to give a "poverty line" for several different family types. The popular estimates were a little bit higher than the official poverty line, and I estimate that roughly 20% of people are poor by the popular estimates.
The survey didn't attach probabilities to the terms, so you can't make a precise comparison between expectations and reality. But if it seems reasonable to me to say that "very likely" is an 80% chance, "fairly" is 50%, "not very" is 20%, and "not at all" is 1%; that gives a sum of 27.8%. So people arseem to be pretty realistic. Of course, there's some turnover in the poor population, so the chance of ever being poor is higher than the proportion of poor at any point in time When you take that into account, people may underestimate their chance of being poor, but not by much.