State Sen. Patrick J. Deluhery of Davenport, Iowa, will be there. So will Mayor Roger McGrath of Laconia, N.H.

But Sen. Charles McC. Mathias of Frederick, Md., will not be there and he is most unhappy about that.

Deluhery and McGrath are among some 6,000 people who have been invited to the South Lawn of the White House today to witness the concluding ceremonies in Pope John Paul II's visit to the White House.

The visit is historic, marking the first time a pope has visited the White House, and it will be the occasion for the largest reception of President Carter's term, dwarfing the 3,000 invitations that were extended last spring to witness the signing of the Egyptian-Israeli peace treaty.

In all, more than 10,000 people have been invited to the White House today to see the pope. They range from the high and mighty of official Washington, who will be on the North Lawn of the White House for the pope's arrival, to little-known Carter political supporters from around the country, who will be among the 6,000 on the South Lawn for the departure.

Mathias, the Maryland Republican, was invited to the North Lawn arrival ceremony, as was every member of Congress. But he had a longstanding speaking engagement before the Maryland Municipal League scheduled for the same time and he was reluctant to cancel that engagement, especially since he is a candidate for reelection next year.

As a result, Mathias tried to wangle an invitation to be among those who will greet the pope this morning at Andrews Air Force Base, which is located in Maryland. He failed, but in a last-minute concession, the White House agreed to include Mathias and Maryland's other senator, Democrat Paul Sarbanes, in the receiving line at the pope's departure from the air base tomorrow night.

Mathias was not alone in his consternation and maneuvering. White House lobbyists on Capitol Hill were pressed for extra tickets by members of Congress hoping to do a favor for a constituent. Interest in and excitement over the impending papal visit could be measured by the spurt in last-minute phone calls asking for invitations, according to White House social secretary Gretchen Poston.

Poston said that receiving a pope at the White House has presented no special protocol demands, only logistical problems involved in overseeing the more than 10,000 invited guests. "He will be treated like any official visitor," she said.

That means that when the pope's motorcade swings onto the north grounds of the White House it will pass between a military honor guard while the White House's "herald trumpeters" mark the arrival with music. But there will be no 19- or 21-gun salutes, reserved for state visits by heads of government or heads of state.

The pope will be greeted at the north portico by the president and Mrs. Carter, and go immediately to a podium on the North Lawn for welcoming remarks by Carter and the pontiff's response.

Most of Washington officialdom will be there for the occasion. Arrayed before the pope on the North Lawn will be members of the House and Senate, the Supreme Court, the Cabinet and agency heads, and the entire White House staff.

The guest list for the arrival ceremony, largely restricted to government officials, was relatively easy to arrive at.But that was not the case in deciding who would fill the 6,000 folding chairs on the South Lawn. For those invitations, a number of factors were considered, including Carter's desire to be reelected.

The White House has not made public the guest list for today's reception, but it is clear that the crowd on the South Lawn will be overwhelmingly Catholic and Democratic. To get one of the coveted invitations, it also helped to be an early Carter campaign supporter, such as Mayor McGrath of Laconia, or a potential supporter next year, such as Sen. Deluhery of Davenport.

Poston and White House press secretary Jody Powell said this week that the Carter-Mondale campaign committee did not directly recommend any names for White House invitations. But over at the committee, a campaign aide had another story.

"We started with a basic list of 200 names, but ended up sending more like 400 names over to the White House," the aide said.

Suggested names for invitations poured into the national campaign headquarters from Carter field offices around the country. The New Hampshire list, for example, numbered about 40 people, including more Democratic state senators (three) than Catholic priests (two).

It remains to be seen how much an invitation for the papal visit will mean in the world of secular politics. The first precinct caucuses in Iowa are only three months away. Deluhery supported the president in Iowa in 1976, but so far has not made up his mind for 1980.

The invitation to the White House, Deluhery said yesterday, is "very thrilling, an honor," but not likely to sway him one way or another.

"It's a thoughtful gesture from the president and his staff, but not something you endorse on or not," he said.

The White House, it seems, realizes that and is leaving nothing to chance. When the pope leaves Washington tomorrow night, Deluhery will remain behind. In the last few days he received a second invitation -- to be at the White House with other Iowans Tuesday for a briefing by the president and high ranking officials on the secular issues of the day.