The Republican National Committee, straining mightily to spend money as fast as it pours in, cannot quite keep up with the deluge.

That is the picture that emerged from yesterday's RNC executive committee meeting, where national chairman Richard Richards reported on a party awash in contributions from a record number of givers and brimming with exotic, state-of-the art plans for spending its money.

The committee raised $28.8 million in the first 10 months of this year, 20 percent above its own projections and 91 percent ahead of the total for the same period of 1979, the last non-election year.

Its expenditures, on the other hand, are lagging behind projections, and Richards reported that the the committee has $7.1 million cash on hand at the moment.

"We have put together the most sophisticated fund-raising apparatus of any political organization ever," Richards told two dozen party leaders from around the country. He noted that the money had been given in 1.5 million separate gifts, with the average gift of $29.

While there was a self-congratulatory tone to the meeting--Richards seemed much like a corporate chairman reporting on a banner year to his stockholders--there were occasional signs of apprehension on what to do with the embarrassment of riches.

For example, when Bernard M. Shanley, a national committeeman from New Jersey, thanked the RNC for contributing a record $1 million in cash and in-kind services to Tom Kean's just-completed gubernatorial campaign, Richards took pains to caution the group that "other governor's races in the future won't get that level of support."

He said the extraordinary investment was made in New Jersey because the race presented a chance to pull together a fragmented state party, and also because, "we had more resources than we typically have."

The revelation of the New Jersey figure caught one of the meeting attendees, Gov. John Dalton of Virgina, by surprise. He said the RNC support for Marshall Coleman in the Virginia governor's was far less, but when asked if he planned to raise the issue with party leaders, he responded dryly, "The election is over, isn't it?"

In a meeting devoted exclusively to the mechanics of party building, one RNC staffer reported on a new video satellite teleconference system the party has just purchased. It will allow a party leader, such as President Reagan, to confer on television with GOP gatherings.

There is also a burgeoning network of seminars for political operatives and candidates. More than 1,600 Republicans have taken part in 26 training sessions so far this year. Next year, specialization will move to new heights when the RNC conducts a seminar the special problems congressional candidates face immediately following a primary.

But the most elaborate presentation, as befit the meeting's overall theme, was on new hardware to raise money. These include the RNC's high-speed presses that will have sent out 27 million letters by year's end and a new computerized phone bank system that will automatically dial the phone and display the contribution record on a screen of past supporters who have not answered 15 consecutive direct mail appeals.