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Today the US House, tomorrow the Senate! Texan Phil Gramm is back in the US House as a Republican. But don't count on him to stay put for long. His staff is gearing up for the '84 elections. The objective: John Tower's US Senate seat. Gramm's campaign coffers are already filling up. But his major hurdle is none other than the senator himself. Gramm expects Tower, chairman of the powerful Armed Services Committee, to step down gracefully after 24 years in the Senate. But Tower has held a series of meetings with supporters, who expect him to run - and win - in 1984. Texas Republicans were badly burned by losing the governorship last November. They're determined not to jeopardize Tower's seat. Observers say Gramm might lose, even with full GOP support. They add that Gramm's record of feuding with Democratic Party colleagues has Republicans wondering whether he can become a dependable GOP team player.

Says one observer, Republicans won't welcome Gramm ''if he comes in as a turncoat and tries to win the top prize first time out of the chute by running against the GOP's only remaining statewide officeholder'' in Texas.m