WASHINGTON (AP) _ President Bush said today he was ''very pleased'' with his primary victories this week despite the nagging protest vote. Challenger Patrick Buchanan vowed to stay in the race ''all the way to the convention.''

''We're doing well,'' Bush said as he left for Florida where another big primary comes next week on Super Tuesday. ''We won everything. And we're going to keep on winning everything. Tough times out there and I think people are beginning to understand that what counts is who wins these primaries.''

Bush won primaries Tuesday in Georgia, Maryland and Colorado, but Buchanan received at least 30 percent or more in all three states following hard- hitting television advertising campaigns by both candidates.

''He is in deep trouble,'' Buchanan said of the president. ''What the party is saying is we want new leadership.''

Bush, leaving the White House for Tampa after attending a private Ash Wednesday service, fielded questions from reporters, agreeing with the suggestion that Buchanan's votes are actually votes against the president.

''It seems to be that way,'' Bush said. He said that once the economy turns around, ''People will see that I'm the person to lead this country, just now as in the past.''

Buchanan, making the rounds of morning talk shows, acknowledged that ''we have to start moving these numbers up, and I need a breakthrough soon.'' But he said it was still possible that the Bush campaign could ''collapse like a house of cards.''

''All he is holding is the Republican base, loyalists who are voting for him because he is the president,'' Buchanan said. ''I am winning all the swing votes that Ronald Reagan and George Bush won to give us our majority.''

The word from the White House on Tuesday night was one of optimism about the president's long-range chances, despite the protest voters.

''President Bush is going to win the nomination,'' said spokesman Marlin Fitzwater. ''He is going to win the election. It doesn't make sense for them to make it more difficult for him. It's not helpful to have this kind of discontent being served by members of our own party.''

But Buchanan pollster Frank Luntz said Republicans need a choice of candidates at their August convention. He said Bush is as weak as Jimmy Carter was in 1980 and ''this time we'll be the big loser'' if the GOP renominates the president.

Buchanan claimed one of his symbolic victories Tuesday in Georgia, although arduous back roads bus tours and slashing television ads failed to lift him above the 37 percent benchmark he achieved last month in New Hampshire.

''The battle of Georgia is now over and it's won. The battle of the South begins now,'' Buchanan told supporters.

Bush advisers anticipate major Buchanan pushes in South Carolina, which holds a primary on Saturday, and in Super Tuesday primaries March 10 in Louisiana, Texas, Oklahoma and Mississippi. Other states holding GOP contests that day are Florida, Tennessee, Massachusetts and Rhode Island.

Bush was flying to Miami and Tampa, Fla., today on the first leg of a six- day trip taking him to most of the Super Tuesday states.

One of the Tampa events was a fund-raising lunch featuring an introduction of Bush by the Desert Storm commander, Gen. Norman Schwarzkopf. Bush has been criticizing Buchanan for opposing the Persian Gulf War.

Buchanan was visiting Shreveport, Baton Rouge and other Louisiana towns today before flying to Tulsa this evening.

No one on either side was predicting Buchanan would win South Carolina or any Super Tuesday contests, even in Louisiana where the renegade GOP chairman has endorsed him.

Instead they said the real showdown in the already brutal intra-party battle could come March 17 in Michigan, a depressed, blue-collar state that Buchanan sees as his best chance to upset Bush.

''We've got to win somewhere. We can't just keep going along with 30 and 35 percent of the vote,'' said Angela Bay Buchanan, the candidate's sister and campaign manager.

Buchanan garnered about 30 percent Tuesday in Colorado and Maryland without campaigning there. In Georgia, where he spent considerable money and time, he was at 36 percent.

''It's certainly embarrassing for the president to be held to the low 60s in his own primary,'' said Earl Black, a Southern politics expert at the University of South Carolina, referring to Bush's 64 percent in Georgia.

But he predicted Bush, with Gov. Carroll Campbell's help, would receive at least 70 percent of the vote in his state's primary Saturday.

''A lot depends on whether the Carroll organization can turn out these voters,'' Black said. ''That may be the problem. There isn't a great deal of enthusiasm for Bush among rank-and-file Republicans.''

Bush said Tuesday night that he understood the message he was getting from voters. ''I hear your concerns and understand your frustration with Washington. I am committed to regaining your support,'' he said in a statement.