<p>(With some exceptions) one can get a job in business regardless of major. You will just need to do a lot of legwork/networking on your own. At worst, you should be able to land a business related position in an industry that is related to your major (ie if you majored in EE, then a tech company, if you majored in ChemE, perhaps something in the energy industry). At best, you could land a job in a field like consulting, where soft skills are far more important than anything learned in the classroom.</p>
<p>Regardless, it is probably going to be difficult to turn down the more lucrative engineering offers. Furthermore, many engineering jobs are business-related. My brother is a chemical engineer, and his first job was chemical sales. He did perform some lab work but most of his job dealt with customer relations and deal closing.</p>