I do not think it looks incomplete since you have plenty of color all around. Usually I will choose a rug to bring in more color, but here it's not needed. The only thing to consider about getting better a rug would be comfort/coziness

A rug would also help to define spaces. But if he's totally against it, I don't think it's so bad in this space

I think it would look nicer with an area rug.

Living room colors and furniture are great, as is the wood floor, good balance of looks and functionality, although I might consider one less couch. I would skip the area rug, it looks nice the way it is. That being said, have you thought about decluttering this space? Way too many things from open shelves, overflowing table, bikes, desk, file cabinet, more cabinets, baskets...just a suggestion; I would try to find a way to simplify this space, leaving only the things I need and either toss or store all else.

Bill, you caught me, we're actually in the middle of a decluttering project right now. The kitchen table is holding the things that need a home. This area is our only living space, so the bikes are going to stay, but the table, kitchen island, and box full of cords are being worked on! I just really wanted to share my interim progress!

I would just look into closed pantry type cabinets for the stuff you need it will eliminate the eye clutter and still serve its purpose. I kind of like the bikes but I would lose the blue painted piece if possible.

Agree about the de-furniturizing this space. It seems every square inch of wall has some sort of furniture or shelf against it. Id say at least 1/2 of your tables/desks/shelves needs to go via Craigslist. You've got a cute living room set thats really pretty and fun but it doesnt do any good if the rest of the space is overflowing with stuff. When I saw the thumbnail of your pic I thought it was a pic of a furniture store showroom lol.
So yes declutter all the stuff -- cotds, books, papers, electronics -- but also consider eliminating some of the furniture housing all this stuff. That will give you the biggest impact in having a nice home

I think it Looks good! Where did you get your sofa table?

Zooming in on your pic, it seems you could easily lose the buffet style piece behind the couch....the blue painted piece with black shelving on top....the little ornamental footstool....the plastic bins....the chest looking piece in the corner to right of tv. Then for your food/kitchen items get something that has doors ie closed storage. From ikea. Eliminate some of the smaller decorative nick-nack items on window ledges. If its smaller than a loaf of bread and decorative, ditch it. Sell all this stuff on CL and go splurge on a nice dinner or whatever. OR splurge on a prettier desk with a little more style to it. I think your place will then look fab!

A lighter rug (is the color soft silver in the chairs?) would ground the space. What you've chosen is lovely. Must be larger than the coffee table top but all legs don't need to sit on it

That "desk" is actually my husband's work bench. We won't have a garage until we transfer and move into a new place 10 months from now. The open loft concept is great, but we'll go for a house next. I realize it looks like a lot of furniture for the open room, but the goal is to be able to move the workbench and open shelves into a garage, and the buffet server will be in a dining room with the kitchen table when we move to a house. I really do want suggestions for the area rug though! Our decluttering is a work in progress, but I'm happy with the amount of furniture we have. Thanks for the suggestions so far!

If you plan on moving in 10 mo tgen I probably wouldn't invest much money in furnitire and rugs etc. Reason being your new house in 10 mo may be completely different layout and the stuff might not work. That being said Id just go with no rug for now esp if your husband prefers it that way

Here are a few suggestions. It's hard to get the color right on a monitor. I wasn't at all sure these are the right color to go with your furniture. But, I think the patterns work.

Wow! I really love the mixture and coordination of patterns you've set up in your living room. I don't think you need a carpet because there is such a great mix of colors already there. I think it would detract attention from the couches!

If you end up getting a rug, do not get it so that just the coffee table sits on it. The general guideline for floating couches is to have the couch entirely on the rug.

Make sure the couches and the chairs can fit entirely on the rug. Measure first.