The most common major at the majority of Ivy League colleges is economics, and a large portion of Ivy League grads first job after college is in investment banking or consulting. If you are in this group that is interested in going in to elite banking or consulting, then an Ivy league name is likely to make things easier.
However, in the overwhelming majority of other industries, the Ivy League name has far less impact. Going to a well known state school instead is almost certainly not going to be a problem with getting your resume through the computer screening. In the survey of hundreds of employers at http://www.chronicle.com/items/biz/pdf/Employers%20Survey.pdf , employers as a whole rated college reputation as the least influential factor for evaluating resumes of new grads and rated elite colleges as less desirable than state flagships for hiring purposes.