Nearly six weeks after the air war in Yugoslavia began, the Senate took up debate today over authorizing President Clinton to use all means necessary to win NATO's fight for Kosovo.

A bipartisan resolution was championed by Senator John McCain, an Arizona Republican and Presidential aspirant, who said the Senate had to encourage the President ''to wage this war more effectively than he has done thus far.''

''If he does not, the shame is on him,'' Mr. McCain said. ''If we lose this war, the entire country and the world will suffer the consequences. Yes, the President would leave office with yet another mark against him. But he will not suffer that indignity alone. We will all be less secure. We will all be dishonored.''

The resolution appeared to be doomed by opposition from the Senate's leadership and was likely to be shelved on Tuesday morning, its supporters said. The majority leader, Trent Lott of Mississippi, postponed a scheduled vote tonight after Mr. McCain criticized a four-hour limit on debate.