We study deformations of the standard embedding of the Lie algebra $Vect(S^1)$ of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle $T^*S^1$ (with respect to the Poisson bracket). We consider two analogous but different problems: (a) formal deformations of the standard embedding of $Vect(S^1)$ into the Lie algebra of functions on $dot T^*S^1:=T^*S^1setminusS^1$ which are Laurent polynomials on fibers, and (b) polynomial deformations of the $Vect(S^1)$ subalgebra inside the Lie algebra of formal Laurent series on $dot T^*S^1$.