Of course you can enjoy this hobby cheaply!
It can be a bit frustrating when you read through the forums and see fellow birders fortunate enough to have $1000 plus budgets when like me $100 can be hard to justify....but I have found perfectly acceptable birding binoculars very cheaply indeed.
My first pair were found in a junk shop that specialised in house clearances. They had a few poor and tatty binos in store, but I chatted to the owner and said I would be interested if she had anything else come in. After a few weeks she called to say she had a box containing all sorts of binoculars, cameras etc. Lo and beheld a pair of Asahi Pentax (8x30) were amongst the pile in the original case, but not having seen use for many years, they were in very good condition despite their late 50s/early 60s vintage and needed only a good clean to bring them into serviceable condition. They are solid, compact, and provide a very sharp image, though the golden coloured coatings did seem to lend a slight colour cast to the image....but, the price...well I paid £7 for them. They really got me interested in birdwatching as a hobby, that was about 4 years ago, and they were the only binoculars that I owned until recently.
I know I was lucky, however, I recently purchased a pair of Opticron Vega II porros (8x40) to replace the Pentaxes as my main pair. The Opticrons were on sale at £35 in a local camera shop, and I was very impressed with the bright image, and the superior contrast (due to the modern full multi-coating I expect).
As a quick footnote I would add that in the UK LIDL supermarket chain occaisionally has binoculars of different magnifications. The ones they sell at present are under the brand name Auriol and are 10x50 (maybe a little too much size and magnification for most birdwatchers but I grabbed a pair after testing them in store as I wanted some 10x binos for use at the coast. I have to say that for the £17 that I paid for them the image is very good indeed. I am writing a review of them at present to post here later.
I hope that this gives you some hope that loads of $$$ do not really need to be spent to enjoy this great hobby.
Regards