Washington — President Reagan is going all-out to save his administration.
Within high reaches of the administration there now is the admission that unless Democratic gains this fall can be held to 15 to 20 seats, the final two years of the President's first term could be marked by legislative ineffectiveness.
''He'll not be a lame duck,'' one key figure in the administration says. ''But he would be less effective.''
Even if losses are held at 15 to 20 House seats, White House political strategists now say the President will have a difficult time putting together the GOP-Democratic coalition he must have to move forward with his spending-cut initiatives.
But should Democratic gains in the House go above 20 and up into the range of 30 to 40, the President will have a very difficult time initiating legislation. He'll be left pretty much with having to exert a negative force on spending through the use of the veto - with the anticipated Republican majority in the Senate upholding his veto.
So the problem facing Mr. Reagan during the fall campaign is clearly this: How is he going to divert voter attention from unemployment and the recession - negative political elements that seem to reinforce the trend normally favoring the party out of power in an off-year election?
The presidential strategy, unveiled at his recent press conference, is simply one of seeking to persuade the public: (a) that they are better off than they were under President Carter (inflation down, interest rates lower), and (b) that they must elect GOP congressmen to make sure Reagan is to be able to lead the country out of what he repeatedly calls the Democratic-inflicted economic morass he inherited.
Can the President do it? Outwardly the administration is talking bravely. Some GOP leaders, including former GOP national chairman Bill Brock and GOP House leader Bob Michel (R) of Illinois, even say that Republicans might come out with a net gain in House races.
But privately, this administration is deeply concerned about its prospects. It sees the strong possibility of the Reagan counterrevolution being badly slowed, if not stopped in its tracks, by the persistent bad economic news.
Will the President's ''Let's-keep-on-course'' theme work? John Sears, the President's former campaign strategist, gives only a qualified ''yes'' to this question.
''It's designed to buoy Republican voters,'' he said. ''It may well help to get the Republican vote out - and that's what they mainly are wanting to do.''
For other voters, says Mr. Sears, a highly respected political analyst, the Reagan pitch will likely be largely ineffective.
''He's been in the presidency too long now to convince (voters) other than Republicans that this recession and this unemployment is the fault of Jimmy Carter,'' says Sears.