The simple IRS administrative rule change could implement e-verify very easily. Require an annual I-9 form which must have the corresponding e-verify number / approval attached. If the number is not attached, the employee is taxed at the highest rate and the business is taxed at a higher rate. Once the e-verify is completed and filed and the employee is found to be legally employees, the tax rate reverts to the correct rate.
We can't even get sensible laws passed that require ID to vote w/o the left screaming that it's a voter tax and/or an attempt to weed out minorities. Requiring substantive proof that an employee is eligible to work within the US would be met with similar opposition and for the same reasons.
Great idea if we could get it done.