The CR has passed the House. There is no Democrat CR.
She is correct that any changes made to the CR, would require it to go back to the House chamber for them to either pass or reject the changes, and then go back to the Sentate chamber of Congress, if the House chamber made additional changes to the CR before they accepted the changes the Senate had made.
They only thing is that it would stop the shutdown once both Chambers of Congres had passed the CR, ans then the Presindent saigned it once he received it from Congtress. How long that would take is dependent upon how fast they could get it to pass both chambers of Congress.