President Reagan spent a chilly, foggy day at his mountaintop ranch near here telephoning conservative "Boll Weevil" Democrats in Washington on behalf of the GOP-drafted budget alternative he favors.

Deputy White House press secretary Larry Speakes said Reagan expected to call about a dozen of the conservative southern House Democrats today in an intensive personal lobbying campaign begun over the weekend to reconstruct the coalition of Boll Weevils and Republicans that gave him budget victories in the House last year.

"He feels that he received some commitments," Speakes said, "although the situation . . . remains very fluid. There are a number of undecided votes, and the outcome is too close to call."

As if to underscore Speakes' point, one of the Boll Weevils, Rep. L.H. Fountain (D-N.C.), didn't return Reagan's call. "A congressman has got to be on the floor during the budget debate, he can't be talking to the White House all day long," an aide said.

Reagan is to remain at the ranch, about 30 miles north of here, until Sunday, when he is to return to Washington for three days before going to Europe for an economic summit at Versailles and a meeting of the North Atlantic Treaty Organization in Bonn.

Meanwhile, the White House announced that:

* Israeli Prime Minister Menachem Begin had accepted an invitation from Reagan to come to the White House for a "working visit" on June 21, three days after Begin is to address a special U.N. session on disarmament.

* Reagan intends to nominate Arthur H. Davis, A Denver businessman, to be ambassador to Paraguay.

* Reagan urged anti-abortion advocates to conduct a memorial service for hundreds of fetuses and embryos discovered preserved in jars of alcohol in a shipping container from a now-defunct medical laboratory in Santa Monica where abortions were performed.The service had been proposed by a doctor in Palm Springs who belongs to an anti-abortion physicians' group.