Washington — The President's diplomatic offensive in Europe is being twinned with a new initiative in the budget battle here at home.
Top White House aides express confidence that they soon will put together a " y -/o/ hat will make it through the House.
''We are very hopeful,'' says Edwin Meese III. Another Reagan aide, heavily involved in liaison with Congress, puts it this way: ''We think it now is doable.''
He says that the Democratic conservatives and GOP moderates who failed to back the Reagan-endorsed Michel-Latta budget resolution last week ''now are listening very intently'' to a new proposal that includes these ingredients:
* Bringing the budget deficit close to and perhaps under $100 billion, mainly by providing deeper cuts into social programs. This is designed to bring the conservatives aboard.
* The new package won't cut heavily into medicare and will probably provide more funds for education than the defeated Michel-Latta proposal. These changes are aimed at making the resolution palatable to the GOP moderates.
Already, the White House, including the President, is well into a new, intensive campaign to put together the coalition that brought the House victories last year. ''We need to pick up about 35 votes,'' says a White House aide. ''And I think we can do it.''
Spearheading the effort to woo Democratic conservatives and moderate Republicans in the House to the Reagan budget plan is Kenneth Duberstein and his congressional-liaison staff.
Right behind them, making calls to House members, are Vice-President George Bush and Mr. Meese.
Presidential chief of staff James Baker will be back from Europe next week to , as one aide puts it, ''lead the charge'' in the budget fight.
''The President won't hesitate to call from Paris,'' a Reagan associate says, ''if it seems necessary.''
One White House aide says that a number of House Democrats and Republicans who failed to support the Michel-Latta plan now ''seem ready to vote for a plan if we include just a few sweeteners,'' one aide said.
Michigan Congressman Guy Vander Jagt, chairman of the National Republican Congressional Committee, says he sees a new Republican budget package that ''by moving just a little to the right'' will bring the conservative Democratic ''boll weevils'' back into a winning coalition.
The Michel-Latta amendment was only one of several approaches to the budget that was voted on and defeated last week. But it came the closest, 235 to 192, to being adopted by the House.
The White House strategy is to move to the right ideologically, seeing this as the only way to pick up the conservatives. The President will agree to providing a few sweeteners to the Republican moderates. But, basically, the President and Republican leadership will rely on wooing these Republicans by applying some pressure on them to ''stay in line.''
The argument that will be used to sway these Republicans, sometimes called gypsy moths, will go something like this: You don't want to go back and confront the voters after voting against the President on the budget. You don't want to face the wrath of Republican voters who will feel you held up the President's efforts to turn the economy around.