Asked if the customs enforcement bill is getting pushed to January, McConnell's office said a vote hasn't been scheduled yet.
Durbin said that if lawmakers try to bring up the legislation it would have to overcome procedural hurdles, which could eat up the Senate limited time remaining.
"It's possible the Republican leadership wants to hold this over," he added, while stressing that isn't his decision to make.
If Durbin were successful in removing the Internet tax ban, it would force senators to send the customs bill back the the House.
- This story was updated at 4:47 p.m.