Upvote:6
The answer depends on the reason for the ESTA denial. If the ESTA was denied because of some fact that makes the traveler ineligible for the VWP, then the traveler is simply ineligible for the VWP, and applying for entry at a land border won't change that.
If the ESTA was denied for some reason that doesn't actually disqualify the traveler from using the VWP, then the traveler might be able to convince the CBP officer at the border to grant admission. This might be risky, however, since the CBP officer will probably know about the ESTA refusal, so will probably scrutinize the traveler more closely than most. I wouldn't try this unless I were very confident that I could establish my eligibility for the VWP.
The safer course of action, if time permits, is to apply for a visa.