1A is too much for a SN754410 unless you cool it with a strong fan or put an ice cube on top of it. The limiting factor for most motor drivers is heat, not the current that's published in the datasheet (see our Motor Driver Myth application note).
The amperage of the power sources doesn't determine the current flow through the driver, it is the motors that determine the load current. A 12V 1.5A supply means that the supply could provide 1.5A if the motors demanded it.
The bridge by no means regulates the current. If you hook up a high-current motor to the bridge and you allow this high current to flow, the driver will be destroyed unless it is a driver with overcurrent protection (which the SN754410 does not have).
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The Rugged Motor Driver: two H-bridges, more power than an L298, fully protected