Blinking led using interrupts in AVR
This is the ATTiny13's interrupt vector table. 



PCINT3 is not an interrupt vector. You need to change that to PCINT0. It looks like you have the PCI and mask set properly. You should be able to make that change and have your interrupts work. You also need to add initialization to make your push button work.

DDRB |= (0&lt;&lt;PB3); //Pushbutton input
PORTB |= (1&lt;&lt;PB3); //Enable Pushbutton pull-up
DDRB |= (1&lt;&lt;PB1); //LED output


That will enable the internal pull-up and allow an edge to happen on a button press. This will likely work for simulation, but a real circuit will need some debounce either in hardware or software.