President Reagan, determined to fight for his No. 1 domestic priority, has asked Congress to stay in session as long as it takes to pass major tax revision legislation this year, Administration officials said. The officials said Reagan may mount a publicity campaign to prevent the Senate from putting off action on a tax bill until next year. If necessary, they said, the President may consider calling Congress back into session to force the Senate to finish work this year. One official described Reagan as "sympathetic" to the political realities of the situation and "the tremendous pressure on the Senate," but he said the President "is quite firm and quite determined."