What colour and shape are the flowers? And does it bloom before, during, or after leaf-out? I agree that some hint about leaf shape would help, As a wild guess so far I'd submit mock orange, or philadelphus... although that blooms in summer I think. There just aren't that many "very" fragrant" shrubs. You might just google "fragrant shrub" and see what you get. The other thing you could do is get a shrub book from the library, and leaf through it - you may recognize it.

opposite leaves, tapering to a sharp point, stems tending to have a redish tint to them. Larger bushes have a weeping habit, and old growth is very woody, rough bark. The ones just now growing here haven't had flowers yet, but the ones they so closely resemble have bright red berries and whitish to pinkish flowers I have spent so many years jerking and burning vine honeysuckle that I totally overlooked the bush varieties. And we also have a low scrubby bush that I have always heard called 'buckbrush' and never really wondered about its real name. It's barely knee-high and has tiny ovate leaves, red berries in the fall. But I think it's something else but stll can't find a match in my books. Funny how when you are surrounded by the same plants all your life you never stop to think about where they came from or if they are harming the natives. I never knew anything about japanese honeysuckle until about 15 years ago. Til then it was something I was pleased to see since it smelled so nice in the summer. After I began trying to thin it out of our woods here, I even had people stop and ask why I was doing that, since it was so good for rabbits and deer and was such a lovely vine. SOmetimes I wish I did not know the difference, because I am now aware that there's no way I will ever win this battle, not even on 5 acres.

if you literally cut it to the ground.. with no insult to the root mass ... it will be near that size again .. in a year or three ... you must use a stump killer.. or get digging ... though i wouldnt use a truck or some such.. as you risk pulling out the sidewalk ... a sharpened shovel.. and a sawzall with a tree blade .. and some good exercise will get you where you want to be ... and if you are going to dig it up ... do not cut it to the ground first.. leave some 2 or 3 foot tall stubs.. so you can use them for leverage ... unless you chip it.. i dont recommend putting this thing in the compost pile ... neighbor tried that with shrub cuttings.. and 5 years later.. had to pull his pile back apart.. as intact wood does not rot very fast ... glad you are getting rid of it... ken

I think it is an Acacia, perhaps A. longifolia, being grown in an atypical manner.