Sounds like you may need an 8 channel USB interface so you can record more that just two sources at once. Some will set ya back but there are less expensive ones too.

I used to use an Alesis SR 16 myself but I've found there are so many other, better sounds out there (more realistic sounding drums) set up as VST-I's.
Also going to be a little difficult using multiple headphones with the Tascam 2X2 unless you have an external headphone amp.
 

Actually Chuck he didn't say multiple, but you more or less need 2 for recording vocals, one for the "Engineer" and one for the "talent",, I used to get away with headphone splitters for this. Radio Shack. 
I agree about using those old drum machines,, must sound horrible. Mine sure does. and nothing worse than a steady drum beat that never changes. It is soooo easy to use Sonar to make a very realistic drum track.  But I make no judgement I've heard worse when real drums were used too. 

Cactus Music
Actually Chuck he didn't say multiple, but you more or less need 2 for recording vocals, one for the "Engineer" and one for the "talent",, I used to get away with headphone splitters for this. Radio Shack. 

 Did I miss something ? He said "My wife and I"...
That sure sounds like multiple to me.

MDShinn
 
My wife and I just want to make great recordings of originals for ourselves.

 
And this...
 

MDShinn
 don't know how to setup good headphone levels that result in good recording levels 

 
Doesn't sound like a Radio shack splitter is the best remedy.
 

Too bad that Tascam unit only has one headphone jack.
 
A headphone amp is relatively cheap.  > https://www.bhphotovideo.com/c/buy/Headphone-Amplifiers/ci/1817/N/3992462087
 
 

I said,, I used to get by not that it was ideal but it works perfectly fine in a lot of situations. 
I myself have a dedicated mixer just for headphones. 
We sort of need to hear more details I guess. 
Like, are you planing on recording songs "live" in one take, or overdubbing each part?