If it sings, soars, cheers or blooms, chances are that President Reagan has received one.

White House spokesmen said yesterday that "hundreds and hundreds" of telegrams, letters, cards and other get-well messages are arriving daily for Reagan from all over the world and in all languages.

Besides bouquets of flowers, a card that sings "Tomorrow" and a telegram signed by 2,000 summer campers in New York state, there also arrived a batch of 200 balloons inscribed "Get Well" from comedian Joan Rivers.

Nancy Reagan, back in the all-too-familiar role she filled in 1981 of paying daily visits to her hospitalized husband's bedside, isn't going empty handed -- she took Rivers' balloons with her yesterday as well as a Snoopy puzzle sent to him by a White House volunteer.

Many of the get-well wishes are from close friends, and Mrs. Reagan personally carries those to Bethesda Naval Hospital, where Reagan is recuperating from cancer surgery.

Other messages come from world leaders and fall into the official category. Soviet leader Mikhail Gorbachev, for instance, expressed his sympathy through diplomatic channels. Another well-wisher was Nicaraguan President Daniel Ortega, whose leftist government Reagan often has denounced and has provided financial support and training for rebels to overthrow.

British Prime Minister Margaret Thatcher telephoned White House chief of staff Donald T. Regan Monday night asking him to deliver her "love, affection and best wishes" to the president. Regan did so yesterday.

Regan also told reporters the president called Mrs. Reagan "a real trouper" during the difficult time. Added Regan, "She's doing remarkably well for a woman going through this emotional experience."

House Speaker Tip O'Neill said on Capitol Hill that "it goes above politics" when asked what the political impact of Reagan's illness will be and added that he was "entirely happy" that Reagan is recovering quickly.

A majority of the president's well-wishers are not names in the news but simply American citizens who want to tell him "we hope you're back up soon," according to assistant presidential press secretary Dale Petroskey.

"Quite a few have come from people who had the same surgery 10 years ago, and tell the president to hang in there, that he's going to do all right," Petroskey said. "Many messages contain prayers and mass cards; some are wishes from people telling him to enjoy the rest. A lot of them mentioned Nancy and how much they like her."

He said the White House "makes an effort to acknowledge" messages sent to the president.

Jennefer Hirshberg, Mrs. Reagan's press secretary, said the first lady received a "very nice, sweet letter" from Sarah Brady, whose husband Jim, presidential press secretary, was wounded in the 1981 assassination attempt.

Hirshberg said that in addition to "lots of flowers," there have been cards, notes and pictures from young patients in the hospital's pediatric ward and that the Reagans were "deeply moved" by their thoughtfulness.

James Rosebush, Mrs. Reagan's chief of staff, said the children had asked the president to pay them a visit, but yesterday Mrs. Reagan substituted for her husband and gave Rivers' balloons to the children.

Hirshberg described Mrs. Reagan as still feeling "drained" by the anxiety over the president's surgery. She said the first lady told her she would be glad when her husband is home again.

Mrs. Reagan's former press secretary, Sheila Tate, said she talked to Mrs. Reagan Monday night and that she "sounds good."

"She mentioned a couple of times that what the president has gone through may help educate people about cancer of the colon. She spoke very highly of the doctors who attend the president," Tate said.

She also said Mrs. Reagan told her that she was continuing with her schedule because the president insisted upon it.

"She's shown a lot of public courage through all of this and I'm proud of her. It's really been hard," Tate said. "I think Mrs. Reagan's brother, Dr. Richard Davis, must have been the most important person in all of this because until he got here, she felt terribly alone."

Tate recalled that when Reagan was shot, the first lady's father, the late Dr. Loyal Davis, flew in to be with her and interpreted medical results and prognoses to her in much the same way his son is doing for her now.

The Reagan children all offered to fly back to be with Mrs. Reagan, but Tate said the first lady reassured them "things would be okay."

Today the first lady flies by helicopter to the USS America, off the coast of Norfolk, to be briefed by Navy Secretary John Lehman and other officials on the Navy's program against drug and alcohol abuse. She will return to the White House tonight.