House committees yesterday began drafting a battle plan for combating drugs that is so ambitious -- ranging from military interdiction to new educational programs -- it could end up costing $5 billion a year, according to congressional estimates.

The new program is being mapped out against the backdrop of a commitment from the Reagan administration to spend $359 million next year to interdict drug smugglers, broaden intelligence gathering and drug prosecution, and spend more money to prevent drug abuse.

The administration's blueprint is contained in a letter that Attorney General Edwin Meese III recently sent to Congress and Vice President Bush. Meese called the $359 million effort "a balanced approach."

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), in calling for an all-out war on drugs, stressed in meetings with Democratic leaders, according to several persons who attended, that he wants a bipartisan campaign and not a Democratic political effort to preempt President Reagan on the suddenly popular drug issue.

Rep. Glenn English (D-Okla.), who as chairman of a Government Operations subcommittee has been focusing on ways to interdict drugs bound for the United States, said yesterday that he could not put a price on the O'Neill initiative but "it is likely to run into the multibillions each year."

English said he saw no indication that either Congress or the White House would propose raising taxes to pay for the program. "There will have to be a change in priorities," English said, "with money coming from other programs."

Sen. Dennis DeConcini (D-Ariz.), who has been allied with English in the effort to push the military into drug interdiction, said last night that he and other senators will introduce a companion measure to the one being drafted for O'Neill. He estimated the annual cost of such a program at between $3 billion and $5 billion.

Although a general tax increase to pay for the effort is not politically palatable, DeConcini said, "enhanced revenues" could be a source of financing. He said he favored increasing tobacco taxes and using the increases Reagan had earmarked for the Defense Department to fight drug use.

Meese in his letter said the administration's National Drug Enforcement Policy Board, which he heads, wanted to work with Congress "to end this national scourge." The board recommended spending the bulk of the $359 million in fiscal 1987 on aircraft to interdict drug smugglers.

The rest of the remaining money would be spent on intelligence collection, drug investigations, drug prosecution and drug prevention.