BJT Saturation with small load/ H-bridge
To answer your question directly, You have both of your transistors in saturation mode. That is not the problem. A quick look at the data sheet from ON Semi's 2N3906 states that the MAX collector current a 2N3906 can sustain is 200mA (same with 2N3904). You will never reach 1A. Please select another BJT pair.