".... unlikely to quickly produce the swift action demanded by Republicans and some Democrats to reduce the overcrowding at the border."
The "root causes" language is a reference to something Harris said: "While we are clear that people should not come to the border now, we also understand that we will enforce the law. We also — because we can chew gum and walk at the same time — must address the root causes that cause people to make the trek."
Walking and chewing gum at the same time is a metaphor,* initially designed to insult someone who can't do these 2 relatively easy-to-do things simultaneously. It doesn't work too much as a brag, unless you're saying that the 2 things are easy to do at the same time.
What are the 2 things? There's a huge difference between wanting people not to come + caring about root causes and effectively enforcing all of the law restricting the border + changing the conditions that are causing people to come to the border.
The first set of things is easy to do, damned near effortless. The second set is nearly impossible, done together or done one at a time. Might as well laugh about doing them together because you know you're not going to make much progress at all on either.
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* "The term is recorded in a Texas newspaper in [1964]. President Lyndon Johnson allegedly said that then-Congressman (and later president) Gerald Ford couldn’t 'fart and chew gum at the same time.' As early as the 1900s, it was observed that women talk a lot and chew gum a lot, but don’t 'talk and chew gum at the same time.' Entertainer and cowboy philosopher Will Rogers was described in 1926 as 'the only man in the world who can chew gum and talk sense at the same time.' It’s probable that the saying 'walk and chew gum at the same time' developed from the earlier 'talk and chew gum at the same time.'" That's at Quora. To speculate more coherently: People said women can't "talk and chew gum at the same time," then some crude fellows thought it was funner to say "walk and fart at the same time" — because walking and farting is a very funny subject. (I've seen George Carlin demonstrate the hilarity.) Then it got turned around for fun to LBJ's "fart and chew gum at the same time." Then it got cleaned up into the present-day corruption, "walk and chew gum at the same time."