It is definitely possible. Checkout Southwest.com for offers as well as
www.i4vegas.com . I also really recommend
www.cheapovegas.com as a source for some great tips. On our most recent trip in January, DH and I went to Vegas and stayed Downtown as well as right off the Strip. Off the Strip we stayed in a great place called Tuscany Suites. Great, HUGE room and at a really great price. Not far from the Strip at all. I also really recommend renting a car. Transportation to and from the airport as well as getting around Vegas can be kind of pricey. We were able to get a mid sized car for 3 days for less than $50 total thru National. Check mousesavers.com for some discount codes for rental car companies (most of which are valid anywhere!) Having a car makes it really easy to go from casino to casino and see some sights away from the city like Hoover Dam, Red Rock Canyon, etc. If you have a car then you can also take advantage of some off-strip food & gaming coupons to help save some money. When we had our car we drove around constantly and spent less than $20 on gas! Much, much cheaper than cabs and far more convenient than the bus/trolley.
Don't rule out staying Downtown. It can be alot of fun as well. The Golden Nugget is nice but can be as pricey as Strip hotels. We stayed at Fitzgerald's and really liked it. It is in a good location, recently renovated & big rooms and really cheap prices (I think we paid $35 a night.) If you are Downtown and you like shrimp, make sure to go to the Golden Gate for their $.99 shrimp cocktail. It is FANTASTIC and really filling!
Make usre to get pick up the coupons books that you can find at practically every check-in or bell services desk. Lots of great coupons for food and gaming in there. Also, always sign up for the players cards. Most places give you some free play when you sign up for their cards!
Two things I recommend you spend a little extra on. First is a meal at Le Village Buffet at Paris. It is absolutely fantastic. My favorite is the breakfast but the dinner is fantastic as well. It is a bit pricey ~$20+ a person but much cheaper than other sit down resturants. Second splurge is a trip to the top of the Eiffel Tower at night. It is a breathtaking view and it is really romantic. I think it is about $9 per person but you can find coupons for it
Vegas is a ton of fun and can be done on the cheap. You just have to do a little more planning. Have fun