Country western singer Tammy Wynette snuggled up to President Reagan before several hundred members of Congress last night and serenaded him with "Stand By Your Man."

"You know," the president cracked later, "I'm going to get a record of that and send it up to The Hill."

But No. 2 on the president's congressional hit parade at his White House barbecue for the nation's legislators might also have been "Pale Moon and Empty Chairs." There were plenty of empty chairs on the South Lawn as the Reagans tossed their windup party of the congressional session. It was a combination of late-arriving members straggling in from The Hill and some last minute "regrets."

The event drew considerable criticism from some Democrats who questioned the president's choice of last night for his party. It conflicted with their big $1,000-a-plate fundraiser that featured former president Jimmy Carter.

House Speaker Thomas O'Neill said the Democrats' dinner had been in the works long before President Reagan's White House party, and he pointedly reminded any Democrats who entertained thoughts of accepting, that even if they could not make the fund-raiser, their $1,000 checks would be welcome.

The White House social office yesterday afternoon counted acceptances from 318 members and 241 other guests, and regrets from 231 members and 247 other guests. The White House provided no breakdown by political parties but there are 287 Democrats in the Senate and House.

Spokespersons for some Democrats listed among the acceptances expressed surprise.

"I don't even think she responded," a spokesman in Rep. Pat Schroeder's (Colo.) office said.

"Absolutely not," said a spokesman for Sen. William Proxmire (Wis.). "He'll be in session and then will go home."

"He didn't say yes and he didn't say no. He left them hanging," said a spokesman for Rep. Peter Rodino (N.J.).

"When he found out his kids weren't allowed, he decided to go to the [DNC] gala," said an aide to Sen. Paul Tsongas (Mass.).

Some Democrats, however, who planned to make it to the White House, included Rep. Clement Zablocki (Wis.). Said an aide: "In the past he's skipped the DNC dinner, he's been to so many. He does more on the phone than sitting at the table with those people."

For those who did show up, there were 700 pounds of New York steaks grilled over an oak fire by a team of guest chefs headed again this year by Santa Barbara insurance executive Bob Herdmann. Picnic tables were set up around the lawn and festooned with pumpkins and other symbols of autumn.

The president called his guests "an historic Congress" and said they were a tribute "to a form of government that can move from one base of economics to another without upsetting the political freedom we all love so much."

He said his 20 months in Washington had enabled him to know many of them and even on the Republican side he had learned not to take them for granted. "One thing you can't be called is a rubber stamp. I found that out on the tax bill."

Wynette shared the evening's entertainment billing with pianist Roger Williams, both of whom agreed to see to it the show went on after the White House last week canceled an appearance by Beach Blanket Babylon, a San Francisco cabaret show, because it is a non-union production.

"He wanted to do it," said Louise Williams of her husband, who flew to Hawaii immediately after his performance.

Wynette also juggled her schedule to accommodate the White House. "I'm honored," she said, describing herself as a Gerald Ford fan but a Carter supporter ("his being from the South, you know") though most of the time voicing no opinions on politics.