Chuck Fairbanks leads his New England Patriots against the Houston Oilers in an American Football Conference playoff game here on Sunday with the pressures mounting by the hour.

If the Patriots give a disappointing performance in the 1 p.m. contest (WRC-TV-4), he figures to be charged with preparing for the game with the mind-set of a "lame-duck" coach because of his previous announcement that he was going to leave the New England club to become head coach at the University of Colorado.

If the Patriots beat the Oilers, Fairbanks will be obligated to stay with New England for at least another week and continue to lose valuable recruiting time at Colorado, if that is where he is eventually going.

Under the threat of legal action, Fairbanks was persuded to put off joining Colorado as long as the Patriots remain in the playoffs.

Should the Patriots make it through the AFC championship and to the Super Bowl it will be Jan. 21 before he knows whether the New England club will go to court to try to make him honor the remaining four years on his contract, plus an option year.

Fairbanks announced, before the last game of the regular season, at Miami, that he was resigning, and the Patroits loss to the Dolphins.

When he was persuded to return, the consensus among the players was that they would be a better team against Houston with him coaching on the sidelines.

Whether he can rouse the players to the utmost effort after indicating a desire to leave remains to be seen.

Colorado obviously considered that Fairbanks' nature as a successful pro coach would help the recruiting of quality players who have future ambitions to play professionally.

A subparshowing by the Patriots in the playoffs is almost certain to stir criticism of Fairbanks' handling of the affair.

The Patriots built an 11-5 record in qualifying for the playoffs to the Oilers 10-6.

New England finished the regular season No. 1 in total offense and No. 1 in running in the National Football League, and No. 4 in passing. On defense they were fourth overall, second against the rush, and eighth against the pass.

But Houston has a head of steam after eliminateing Miami, and Dan apsto-rini's passing has taken some of the burden off running superstar Earl Campbell.

The new momentum may compensate for the Oilers' otherwise unimpressive team statistics. CAPTION: Picture, William Sullivan, president of Patriots, left, listens as Coach Fairbanks discusses decision to remain with team during NFL playoffs.