Here in the US, if a homeowner doesn't maintain the sidewalks in front of their home and someone gets hurt, we are liable, right? At what point does our government bear responsibility for poor/dangerous infrastructure?
The answer to the first question you asked depends on the state/locality. Where I live, it's not true, but I know it's true in other places (although I wonder about the extent to which responsibility extends).
As for the second question, governments at all levels (federal, state and local) enjoy sovereign immunity. However, both the federal government and all states have enacted tort claims acts that allow limited tort claims (i.e., claims for negligence and other things not arising out of contracts) against them (the state laws also apply to local governments). For example, when a person causes a car accident through negligence and is acting in the course and scope of his/her employment, his/her employer is vicariously liable for the damages. These sorts of suits are allowed against governmental employers under most (if not all) tort claims acts. On the other hand, where damage results from a discretionary decision (e.g., a decision to shore up a bridge foundation), the suit would not typically be allowed.
If I had to guess, I would guess that the Maryland Transportation Authority will not have any liability here.