I need to write an argumentative research paper about "I Stand Here Ironing" by Tillie Olsen. I need to have a thesis that makes an argument. (It needs to be debatable.)

An argumentative essay and a research paper are generally two different types of written works. It seems that your assignment is for an argumentative essay. A thesis statement that lends itself well to debate takes a strong position on a topic. A research paper also will have a thesis, but the paper itself will be supported with evidence from a wide variety of sources rather than just from within the primary text.
The central character in Tillie Olsen’s story is a mother who has tried to do the right things to raise her daughter, Emily, who is now a young woman about to finish school. The mother reflects on many events in Emily’s life that have brought them to their current relationship. Emily seems to be an indifferent student and may be in trouble at school, as suggested by the letter that a school staffer has sent to her mother.
The mother, who is the first-person narrator, is reflecting on the past more than planning for the future. She seems to regard the future as Emily’s province to determine on her own. Although it becomes clear to the reader that the mother will not actually write a response and send it to the school, the array of topics she covers in her meditations concern diverse aspects of Emily’s upbringing.
In terms of a thesis that a writer could support, it will be necessary to decide what you think the author wants the reader to take away from the story. The mother acknowledges errors that she made in her parenting, but she also provides the context—the United States during the Great Depression—for the lack of services to help single mothers and poor families at that time. One thesis would see the family as deeply troubled and hold the mother responsible for the failures. A different thesis would assess the underlying responsibility for these problems on the society, which provided few or, in some cases, no alternatives for child care and health care that a working mother could access. Both potential theses could be well supported from the evidence in the story.

The story is about a mother’s sense of resignation over how she raised her oldest daughter. The key line in the story is toward the end: “So all that is in her will not bloom—but in how many does it? She will have enough left to live by.” It poses some fundamental questions about womanhood, motherhood, and the responsibility of society to help individuals reach their full potential. Here are a few questions that come to mind:
How does the story define “motherhood”? Does the narrator consider herself to be a “good” mother?
What role do the economic conditions Emily is born into (poverty, the Great Depression) play in her upbringing?
The mother is forced to leave Emily in an inadequate day care so that she can work. There are other examples (like the foster home) where institutions put in place to help children like Emily are less than ideal. What is the responsibility of society to help mothers raise children? How has childcare changed from the 1930s to today? 
One of the recurring themes in the story is the mother’s sense that Emily and herself somehow do not meet social “expectations.” To what extent do these ”expectations” inform how the mother thinks about herself and about her daughter?
Here is one final thought: a central image in the story is of the mother ironing, doing what might be called “women’s work.” What does the story think “women’s work” might be? What connections does Olsen make between motherhood and labor?  
Hope this helps! Good luck!