Will White House Fever touch off a feud between two liberal Democratic senators?

Sen. Joseph R. Biden Jr. (D-Del.), has been in the headlines because of his chairmanship of the Judiciary Committee, which will hold confirmation hearings on President Reagan's nomination of Robert H. Bork to the Supreme Court. The pundits haven't decided whether Biden's role will be a plus or a minus in his quest for the Democratic presidential nomination, but there's no question that the publicity has helped his name recognition nationwide.

Now it appears that Biden has found another use for his committee chairmanship: keeping another presidential contender out of the headlines.

Sen. Paul Simon (D-Ill.) is a junior member of the Judiciary Committee and chairman of its subcommittee on the Constitution. He proposed that his subcommittee hold a hearing as part of the city of Philadelphia's celebration of the Constitution's bicentennial.

But as a subcommittee chairman, Simon had to get the Judiciary Committee chairman's permission to hold the hearing. Biden said no.

A Biden aide said the chairman refused because the proposed hearing would have been an "intrusion" into the celebration planned in July by the Bicentennial Committee. But Fred Stein, executive director of "We the People -- 200," the group that coordinated Philadelphia's celebration, told our reporter Gary Clouser that the Simon hearing would have been a welcome complement to the day's events.

Simon's supporters suspect that Biden was less concerned with the intrusion of Simon's panel into Philadelphia's celebration than with the possible intrusion of Simon's mug into the evening news programs and the next day's newspapers.

There was a hint last year that Biden and Simon would not always see eye to eye on major issues. Simon sponsored a balanced-budget measure that lost by one vote; Biden voted against it. The Delaware Democrat's version of a balanced-budget law had been soundly defeated two years earlier.

If a feud is indeed in the making, Biden and Simon have a unique stage on which to slug it out. They are the only presidential candidates who serve on the same committee. (Simon is the only nonlawyer on the Judiciary Committee.) They also share an assignment to the Foreign Relations Committee.

The Judiciary and Foreign Relations committees have publicity potential that other candidates would envy. The Bork hearings will be just the first in a long series of encounters that could make or break either senator's presidential aspirations.

In the months to come, foreign policy will become an issue of overriding importance in the presidential campaign, and the Foreign Relations Committee will be an ideal forum for both Biden and Simon. Since both senators' foreign-policy views are essentially the same, the contest will be more of form than substance, with each man trying to avoid sounding like an echo of the other.

Aides to both senators insist that, while the two men are not close personally, they have great respect for each other's abilities. That rapport will be tested as they share common stages.