While I agree with Joe's answer, I would also like to ask a couple of questions.
Are we talking "posts" as in main support? or are we talking of 'pickets' as in safety barrier between main structural components?
How many feet are included in this stair case? And are you sure of the material of the parts?
I find that most decorative 'pickets' can be welded in place without using nickel rod. But not all, and not if they are the main strength components nor if they are truly a safety factor. If every picket is a decorative cast iron picket, then go with Joe's suggestion without hesitation. If it is a "post" for main support, go with Joe.
I'm just curious about what you are actually welding here because I have seldom used cast decorative posts on railings. Forged steel. Small cast decorators. Small alum decorators (both of the previous with small steel tabs inserted in the casting to accomodate welding in place on the steel.
The use of nickel rod will slow you down considerable, BUT, if the parts are what you say then it is worth it for safety.
Have a Great Day, Brent