The issue is trust. Why should voters trust that Kamala Harris will implement immigration policies they want? Why should they expect her not to yield to the most extreme elements in her party, which believe that borders are a fiction and should not exist? Look at Barack Obama's "evolution" on gay marriage over the course of his political career. Now take an issue that is far more important than gay marriage - how is she going to stop unlimited unskilled immigration? How is she going to stop fraudulent claims of refugee status? How is the whole immigration problem itself going to be solved, if you posit that every one of the 10 million "unauthorized immigrants", and every one of the refugee claimants, needs multiple appearances in court to resolve their situation?
It seems to me that many US people want their cake and also eat it. Cheap workers are good, but also illegal immigration is bad. You kinda need to pick one.
Every job (as an employee) I've ever had has required me to submit IRS form W-9[0] on my first day of employment (or before). It's a standard part of the on-boarding process. To clarify, the W-9 form is to provide your "Taxpayer Identification number" (TIN) to those who will be handling payroll/tax withholding (that is, your employer).
If you cannot provide a TIN, you are not allowed to begin working. If you don't have a TIN, presumably you don't have the right to work. Or is there something about the UK's processes I'm missing?
People apparently feel that the Dems are pro 'letting everyone in' -- an understanding created not just by what the Dems say and do on the topic (and others) but what their opponents say too.
If they don't want people to think they aren't pro-immigration then the Dems have dropped the ball on their messaging and actions.
For a similar and reasonably concrete example, the 'Harris is for they/them' ads and their impact is a worthy case study.