English/Phil undergrad...interested in Political Communications MA

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I'm a senior at GWU, and I've shifted my aspirations a lot. Originally, I had a deep interest in English and Literary Theory, but I've grown somewhat disenchanted with the idea of an academic career. I've always had a really strong interest in politics, but I'm starting to see Poli Comm as a unity of my interests which were scattered across a few disciplines. My interest in English has more or less waned to the political end of things (Marxist theory, rhetoric of politics and media), and Political Philosophy was always my biggest area of interest. I'd like to take the degree into political advocacy or media strategy of some sort.

What concerns me is the fact that I'll be graduating with a dual liberal arts degree and no relevant internships/jobs. I helped found/led a student organization for a year, spent a semester abroad, did English research, and am doing two majors, so between all that, I simply never found the time. I'm concerned that this lack of experience, combined with the fact that my degrees are from a fairly different field, could prove to be a kiss of death, admissions wise.

I'm set on applying, but am I facing an uphill battle?