A new poll by CBS News suggests that if Democrats were hoping the crush of illegal immigrants at the U.S. border would spark a “blue wave” in November’s midterms, they might need to come up with a new strategy.

Democrats are seeing their lead over Republicans in a generic ballot preference shrinking, even in a poll conducted during some of the most intense media coverage of illegal immigrants and the fate of their children when crossing into the U.S.

The CBS poll, conducted in partnership with YouGov, found Democrats holding a four-point advantage — 40 percent to 36 percent — when respondents were asked which party they would like to see win control of Congress in November. The remaining 24 percent of respondents replied “doesn’t matter” to the question.

By comparison, an NBC poll asking the same question at the beginning of June found 50 percent of respondents wanted to see Democrats take control of Congress, or 10 points higher than Republicans.

That’s a 60 percent drop in the margin enjoyed by Democrats in about a three-week period, suggesting either poor methodology by one of the two organizations, or the fact the immigration crisis has not hurt Republicans as they prepare for the midterms.

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When asked if the situation happening to detained families at the border would impact their votes in November, 53 percent of respondents said it would not. While 28 percent did say it would make them more likely to vote for a Democrat, 19 percent said it would make them more likely to vote for a Republican, meaning the current border…