There I have to agree with you. Most Democrats do not support "open borders". In fact, most Democrats think the border situation is a problem and that the government has done a poor job of handling it:
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66% of Democrats consider that the border situation is a "Crisis" (22%) or a "Major Problem" (44%). Only 7% of Democrats say it isn't a problem.
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A big majority of 73% of Democrats say that that US Government is doing a bad job dealing with the border situation.