At any time after the Director of OMB issues a final sequestration report under section
904 of this title for a fiscal year, but before the close of the twentieth calendar day of the session of Congress beginning after the date of issuance of such report, the majority leader of either House of Congress may introduce a joint resolution which contains provisions directing the President to modify the most recent order issued under section
904 of this title or provide an alternative to reduce the deficit for such fiscal year. After the introduction of the first such joint resolution in either House of Congress in any calendar year, then no other joint resolution introduced in such House in such calendar year shall be subject to the procedures set forth in this section.