For four-year degrees, how important is it to graduate in four years? Does it depend on your major?

I'm in a bit of a pickle. My adviser mistakenly told me that I could minor in math and major in engineering by simply taking the upper math classes required for the minor. However, there is a prerequisite that I must take and, ultimately, my graduation would be held back about a semester. I've tried finding many ways of expediting my graduation if I were to do research and get a minor in math, like taking summer courses, but there doesn't seem to be a way around that.

I've been doing so well these past two semesters (about a 3.6 cumulative. gpa), especially in math (I haven't had anything lower than an A in any of my math classes) that I was accepted into a research program where they're going to let me do research in math. I've yet to decide, still, but it'd be either a pre-harmonics analysis research or research in fractals (I'd go to grad school afterwards and hopefully be able to find applications of either research topics to engineering).

However, if I can't graduate on time, will that affect me when applying to grad school, even though I was minoring in math and doing research? I'm currently majoring in mechanical engineering and I don't want a late graduation to affect me for grad school or a job if I decide later on I don't want grad school.

I guess what I'm essentially asking is if graduating with a minor in math and with some research done would outweigh graduating a semester or two late in terms of either going to grad school or getting a job.

The only reason I wouldn't consider going to grad school is because it would mean more time in school and not beginning a career soon. Originally, all I wanted to do was go to school to get a good job and make money. But I've become more interested in research and I know it's something I would enjoy and something that would ultimately pay off more, job-wise, in the future.