I’d say the comparison to jaywalkers is inapt. I’d say the comparison — well, no; not comparison; the thing itself — is summed up here: “A majority of Americans see an ‘invasion’ at the southern border, NPR poll finds”. And I, as it happens, agree with the majority on this one.
You say that we, as, a nation, shouldn’t be straight-up murdering undocumented immigrants before we figure out by due process which ones are okay to come in; I say, make it clear to them that they can apply to come in via a legitimate process, or that they can follow the example of invaders who’ve shown up at the border and gotten killed upon disregarding the equivalent of a warning shot — and that we recommend the former, but that it’s their choice if they want to choose Option B — and if they decide to enter the Do Not Enter Or You Will Be Shot area, shrug with indifference and honor their choice.