When Chief of Staff Howard Baker opened the White House staff meeting Monday by expressing ''bewilderment'' over reported disagreement with Attorney General Edwin Meese III, architects of President Reagan's Supreme Court strategy sighed in relief for the second time in four days.

The first time was Friday, when, just as they had all but given up hope Lewis Powell would quit in time for a Reagan appointment, the esteemed 80-year-old justice did so. But that relief was short-lived. Reports seeped out that Baker was not happy about long-standing Justice Department plans for Appeals Court Judge Robert H. Bork, the distinguished conservative legal scholar, to get the next vacancy.

But when Baker started the new week by denying any conflict with Meese, the Bork express rolled. Meese and Baker conferred, then joined the president. They were ratifying a tenacious strategy to extend Ronald Reagan's reach far beyond his presidency. Bork has always been integral to that strategy.

Meese, backed by aides, determined before the 1984 election that the two right-wing dynamos of the U.S. Appeals Court for the District of Columbia -- Antonin Scalia and Bork -- would get the next two court appointments. As we reported a year ago when Scalia was named to the first vacancy, it was not an either-or proposition.

At that time Powell, who had suffered prostate cancer, was expected to resign in short order, opening up a seat for Bork. But he told friends he had no intention of quitting. As the months left to Reagan dwindled, so did chances of the Senate's confirming anybody but a non-ideological middle roader.

The administration's Bork backers had all but given up when, a half-hour before the world learned it, they were informed of Powell's resignation. The year's delay had been costly. In addition to less time and Reagan's losses from the Iran-contra affair, zealous presidential campaign jockeying by Democrats shaved Bork's confirmation prospects from certain to probable.

The tension also was raised because Powell, always a swing vote, in his last months swung increasingly to the liberals on noneconomic issues. Judiciary Chairman Joseph Biden, highly politicized as a presidential hopeful, says that his virtual endorsement of Bork a year ago no longer holds because he would upset the court's ''balance'' as Powell's replacement.

It was during speculation about Bork's ''confirmability'' that word drifted from the White House that Baker would challenge Meese -- returning from a mission to Germany -- in judge-selection. One White House aide was quoted saying the president should not squander fallen prestige on a tough confirmation fight when what he really needed was a new arms control treaty. Whispers spread about Bork's age (60), weight and heavy cigarette smoking.

But at the Monday staff meeting, Baker sought to dispel notions he was wrestling with Meese for the president's soul. His closest lieutenants also denied it.

In fact, disposing of Bork raised as many problems as it solved. The most widely reported conservative alternative had been Sen. Orrin Hatch, considered the likely nominee if the vacancy occurred in the 1988 election year, when Senate confirmation would be toughest. But administration officials sadly concluded that his vote on raising judicial salaries constitutionally barred him from the court.

With other senators equally ineligible, only a sitting federal appellate court judge was to be considered. Patrick E. Higginbotham of the 5th Circuit in Texas was high on the Justice Department list as a young (48), conservative southerner (replacing Virginian Powell). But the anti-abortion movement announced it would fight both Higginbotham and another young conservative, Richard Posner of the 7th Circuit in Illinois.

Acceptable to the pro-lifers, besides Bork, were Anthony Kennedy and John Noonan of the 9th Circuit in California and former Sen. James L. Buckley, Bork's colleague on the D.C. Circuit. But none was on the administration's Grade A list.

In truth, ''confirmability'' of any conservative is suspect. In opting for a new justice no more Reaganite than Powell, Biden and other Democrats are trying to limit the president's judicial clout on Jan. 20, 1989. Bob Bork, informally tapped nearly three years ago, quickly grew in stature as the administration's only choice if Reagan were not to beat a retreat.