Last time I checked, the Constitution gave the elected representatives of the people the right to decide whether to impeach public officials for failure to comply with completely lawful subpoenas and appropriate oversight. They even provide Congress with immunity included in the Constitution to prevent threats from people like Rosenstein.
As the proposed questions for President Trump from special counsel Robert Mueller imply, just the act of the president raising issues or even having negative thoughts about the appropriateness of actions by Rosenstein, fired FBI director James Comey or Mueller can be investigated as possible obstruction of justice.
This government within the government has now crossed a line that is unacceptable. By gaining the recusal of Attorney General Jeff Sessions, Rosenstein stepped into the shoes of the attorney general, even though he was not appointed to that role by the president.