In other words, no restriction whatsoever on who can physically enter the country. I can't speak for everyone who opposes this, but some of the larger concerns with such a policy are:
1 - Crime - If non-citizens are coming into the country with criminal/violent behavior, deportation is obviously not an option with open borders. Pursuing and detaining criminals who have zero documentation is also a significant challenge.
2 - Resource consumption - Resources are finite, and most require taxpayer funding to some degree. An inflow of non-citizens who pay no taxes puts a strain on the availability of those resources to those are citizens who taxes fund said resources. This would become an enormous issue if the U.S. were to move towards any form of government-funded healthcare, for example. Bottom line, you create a supply/demand issue by leaving immigration unchecked.
3 - Disease - We have a pretty standard set of vaccinations in this country. Our Immigration laws prevent non-citizens from entering the country with certain diseases and without proper vaccinations. This protects the general public's health. Open borders would essentially nullify this protection.
I could go on, but I can't tell if you really wanted to discuss this or are baiting someone.