3:9 I will make those who are of the synagogue of Satan, who claim to be Jews though they are not, but are liars—I will make them come and fall down at your feet and acknowledge that I have loved you.
(continuing from the previous verse)
The accusation here is of lying about the authenticity of the Messiah (synagogue of Satan is the symbolic counterpart). Refresh yourself in Revelation 2:9 where the Smyrna church had outright blasphemy. The Philadelphia church had its Jewish subverters too; only they were more subtle.
come and fall down at your feet
This is not a reference that unbelievers will reverence believers. That kind of bowing down is reserved for Christ ONLY (Philippians 2:9-11). This reference is more like Joseph in Egypt where his brothers eventually fall down before him (not knowing who Joseph was) and beg for food (Genesis 44:14-17). The subtle Jews causing subversion will come and bow down at the feet of the true believers. It is a form of repentance.
and acknowledge that I have loved you.
It was this LOVE that caused Jesus to lay down His life for us (John 15:6-13). Am I able to lay down my life for my friends? If I find it difficult to worship God regularly, to study His Word daily, and to "pray ceaselessly", how will I find the spiritual strength to show this "greater LOVE"?