to answer your question, yes it can be done ...... now whether or not you'll like the way it would have to be done or the cost is another issue.
you did not state whether you would allow any columns to support the beam or not. typically the longer the beam span the deeper the beam. the deeper the beam the more the cost. make sense?
there is no way for anyone on a forum to determine the size of the beam or the construction of the beam (structural composite, steel, solid sawn). the reason no one can do this online is because it requires an evaluation of your existing structure, to determine the direction of floor joists and roof rafters and where these loads are transferred through the structure down to the foundation. if the second floor joists are resting on the wall where you want the beam the more load the beam must support. likewise, if the roof rafters bear upon the wall where you want the beam the more load the beam must support. make sense?
if you desire to open this wall up you would need to contact a local professional engineer that specializes in building construction. they would be able to come to your home and perform an analysis of your structure, plus they would be familiar with the building codes you must comply with. they would be able to investigate your existing construction to determine the proper size beam, methods of transferring the load to your foundation and prepare stamped drawings that you would not only need for the building permit, but for your builder to know how to properly perform the construction.
I myself would not recommend this as a DIY project. A little mistake on your part could create a partial/total collapse of your home. To me not worth the potential of saving a little in costs. Plus I would doubt your insurance would cover this unless you are a licensed builder.
And only you can judge if the total cost is worth what you would get in return.
I know this didn't provide you with the size of beam you'd need (do not think away would attempt to do so on here) but hopefully I have pointed you in the direction you need to follow. One last thing, if you ask long enough and on enough websites you'll get someone that will spec out a beam for you. Of course you do not know them, their level of knowledge or experience. You have to ask yourself one question, "Are you willing to bet your family's safety and your financial investment on someone you do not know or trust?"