I consider myself a liberal Democrat and I am in favor of strong border security and preventing illegal immigrants from entering the country. I don't see this as a Democrat or Republican issue at all, but, rather, a national security issue. From the article, this also seems to be the case, with majorities of both parties in favor of using US troops at the border.
This should be one issue that both parties could work together to solve. Unfortunately, politics has become so fractured in the US that even issues like this languish for years, from presidential terms of one party to terms of the other party, with not enough getting done, for fear one party or the other will receive credit.