There really isn't enough info here to to make any judgments.
I'm assuming this is a one story house?
What is that perpendicular wall carrying?
For starters, you're going to need footers in the basement under the studs that will carry the jack studs that hold the header that is going over the stairs.
As I read that last sentence, I realize this is a tough question to answer over the net.
You'll find more structural framing guys at
but they (and I) will tell you to pay for an engineer.