It is only those persons who come completely within our jurisdictionExactly.
Now let's see what the US State Department says about dual nationals like Obama..."Claims of other countries on dual national U.S. citizens may conflict with U.S. law, and dual nationality may limit U.S. Government efforts to assist citizens abroad. The country where a dual national is located generally has a stronger claim to that person's allegiance. However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws"
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html
Those born dual nationals, like Obama, are NOT born completely within US jurisdiction. As the US State Department declares, either country to which the dual national owes allegiance has the right to enforce its laws, and dual nationals are required to obey the laws of both countries.
It is only those persons who come completely within our jurisdiction, who are subject to our lawsSenator Trumbull is clear that he means to exclude only those "not subject to our laws." You never answered - are you claiming that someone born on American soil of a (non diplomat) foreign father is not subject to US laws on American soil? Again, I urge you to read the whole of Senator Trumbull's comment, of which you are quoting a tiny portion, out of context. Congressional Globe, Senate, 39th Congress, 1st Session Page 2893 of 384.