While there are already web wallets linked to your mobile number, if Bitcoin itself gets linked to a mobile number then you'd pretty much have Paypal. Bitcoin is advertised to be pseudonymous and unreversible. If you link a number your identity would be then linked to the address killing pseudonymity and it would also be possible for anyone with access to your phone number (remember the phone company and the government probably can, along with anybody who steals your phone) could spend your BTC without a private key.

Long story short: It wouldn't go well. If you really want this then just use a web wallet that already supports it.