Made my homework, the huge problem was the steel pact between germany and italy as austria hoped an alliance between them and italy. An other one was the mobilisation of the german troop near austrian border before the referendum, hitler intention were clear: annexion. With Italy more on german side, as well the british ambassador in berlin ( to prevent ww2), Austria is almost isolated.
The best hope for independence is the mobilisation of their army and the prevention of the coup attempt by the nazi party of Austria.
Schuschnigg always stand is ground, even face to hitler, so he need to resolve this diplomatically. With the (rigged) referendum against Anschluss, he have at least three cards on his hand. The first one is the emprisoned member of the nazi party and seyss-inquart, the second one is the menace of a tough war ( the army being fully mobilised) and the third one is the rejection of the "german unification" by the austrian population.
By preventing an easy invasion, he may force hitler back to the negociation table and the rejection of the anschluss may force Neville anderson (the british diplomat) to revised is pro-german policy, thus opening a door for ann international support.
Again, lot of "may", as i dont have enough knowledge about the mens and the spirit of the era, if you guys have informations, feel free to share it !