One major obstacle to Lady Macbeth's plan is Macbeth himself. She initially fears that he is "too full o' th' milk of human kindness" to consider killing the king in order to take the throne (1.5.17). She turns out to be wrong -- he is willing to consider it -- but after Macbeth has had time to consider all the reasons he has not to kill Duncan, he tells her, "We will proceed no further in this business" (1.7.34). Lady Macbeth must then convince him to overcome his scruples.
Lady Macbeth's own scruples and feelings present another obstacle to her plan. She actually prays to be "unsex[ed]" because she wants to rid herself of any "remorse" she might have; likewise, she wishes to squash any compassion or womanly feelings that might prevent her from acting brutally (1.5.48, 1.5.51). Then, when she goes to kill Duncan, she cannot. Alone on stage, she says, "Had he not resembled / My father as he slept, I had done 't" (2.2.16-17). So, it seems that Lady Macbeth is not quite as hard-hearted as she'd like to be, and her compassion -- however small -- presents another obstacle to her plan.