There's only two problems with this: first, the Third Amendment discusses quartering troops, and second, a House Resolution wouldn't raise Third Amendment questions.
Here is what the Third Amendment actually says:
Amendment III: No soldier shall, in time of peace be quartered in any house, without the consent of the owner, nor in time of war, but in a manner to be prescribed by law.
2.) What does the 7th, and the 11th Amendments say?
In "Bad Moon Rising", Oliver Babish's staff is fasinated with the Third, Seventh and Eleventh Amendments. So what does the Seventh and Eleventh Amendments say?
Amendment VII: - In suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise reexamined in any court of the United States, than according to the rules of the common law.
Amendment XI: - The judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against one of the United States by citizens of another state, or by citizens or subjects of any foreign state.
3.) What does the 25th Amendment actually say?
In the fourth season finale, "Twenty-Five", President Bartlet invokes the 25th Amendment by temporarily removing himself from power and handing it over to the Speaker of the House. Some people doesn't know what the Amendment says, so the text of the Amendment is below:
Section 1 - In case of the removal of the President from office or of his death or resignation, the Vice President shall become President.
Section 2 - Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.
Section 3 - Whenever the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that he is unable to discharge the powers and duties of his office, and until he transmits to them a written declaration to the contrary, such powers and duties shall be discharged by the Vice President as Acting President.
Section 4 - Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
Thereafter, when the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that no inability exists, he shall resume the powers and duties of his office unless the Vice President and a majority of either the principle officers of the executive department or of such other body as Congress may by law provide, transmit within four days to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office. Thereupon Congress shall decide the issue, assembling within forty-eight hours for that purpose if not in session. If the Congress within twenty-one days after receipt of the latter written declaration, or, if Congress is not in session within twenty-one days after Congress is required to assemble, determines by two-thirds vote of both Houses that the President is unable to discharge the powers and duties of his office, the Vice President shall continue to discharge the same as Acting President; otherwise, the President shall resume the powers and duties of his office.