There are several most common sources of support that a department can give to their grad students:
Realistically speaking, the best that a student in your situation can hope for is a TA-ship. While the department is not going promise you a TA-ship now, come Fall, it is quite likely that they will find themselves short on TAs for scheduled classes. (How does this happen? For instance, some grad students cannot come because of a variety of problems, say, cannot get a visa, or some faculty get grants and they need to hire GSRs who are scheduled to work as TAs....) In this situation, the department will be eager to hire even grad students from other departments or, even some advanced undergraduate students. Thus, during your conversation, make sure that the department knows that you are willing and eager to work as a TA, that you have some qualification for this (tell them which, for instance, maybe you worked as a grader or you provided mentoring to other undergraduate students). Ask them to put your name on the wait-list (if they have such) for a TA-ship in the Fall semester/quarter. Assuming that this works in Fall, make sure you do a good job, so they might be inclined to offer you a TA-ship in a similar situation in the following semester/quarter.
Edit. Of course, it is quite possible that the department routinely admits substantially more PhD students than they can support (I know some departments that do so; my own department, in contrast, is rather conservative in its graduate admissions process) and, understandably, prioritizes these over MS students when distributing extra available TA-ships. In this situation, there are always Phd students in need of TA-ships and MS students never get these. However, the right thing to do is to find out the exact situation. You loose nothing by asking questions.