Spinning the notion of what makes a wireless carrier on its head, Republic Wireless today announced its “Hybrid Calling” network, which offers no-contract talk, text, and web access for just $19 a month.

The company likens its network to hybrid cars — instead of relying entirely on expensive cellular bandwidth, Republic Wireless has built its phones to utilize Wi-Fi networks whenever possible.

Most of us are surrounded by Wi-Fi connectivity at work and home, so it makes sense to rely on those cheaper (and much faster) networks. Once you leave a Wi-Fi network, the company’s phones switch to traditional cellular access (relying on Sprint’s network).

“Wi-Fi is ubiquitous and cheap,” Republic general manager Brian Dally said in a statement today. “Cellular spectrum, by contrast, is expensive and controlled by the few. So we inverted the status quo, routing everything over Wi-Fi whenever possible and relegating cellular to its proper place – when we are outside of the home, office, or hotspots.”

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The company says it won’t charge overage or roaming fees when subscribers are on the cellular network. You’ll have to pay $199 to sign up for Republic’s service, which provides you with an LG Optimus Android smartphone and a month of free service. After that, you only have to pay $19 a month, with no contract or termination fees to worry about.

As part of Republic’s fair use policy, each subscriber will need to operate at least one Wi-Fi connection of their own. That shouldn’t be a problem for anyone who already has a home internet connection though.

Hybrid Calling is an interesting solution to the industry-wide problem of scarce cellular bandwidth, but it remains to be seen if the company can stay afloat with its uber-cheap plans.

Republic Wireless is a subsidiary of the Internet phone and services company Bandwidth.com.