MX missile opponents, trying to counter Tuesday's 219-to-213 House vote to let President Reagan build an additional 21 missiles, yesterday made an "all-out attempt" to reverse the situation when the House votes again today on the issue.

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who described the effort, said the focus was on persuading some moderate and conservative Democrats who supported the missile to switch positions because of the high cost of building the missiles and hardening the silos in which they would be deployed.

"That's the only argument we've got out there," said O'Neill, who opposes the MX. "It comes down to the fact that a lot of conservatives in my party will have to look at the price tag." Sixty-one Democrats sided with the president and against the Democratic leadership to support the MX missile on Tuesday.

Meanwhile, administration officials and MX supporters in the House began a counter-lobbying effort to hold the pro-MX margin and possibly pick up some of the 24 GOP lawmakers who voted against the missile.

More Republicans voted against the MX Tuesday than in any previous vote.

White House spokesman Larry Speakes said yesterday that "the outcome of the MX vote . . . is by no means certain." He said Reagan would continue his personal lobbying effort "as needed."

Secretary of State George P. Shultz telephoned Republican and Democratic lawmakers who had supported the MX, including Reps. Roy Dyson (D-Md.) and Steny H. Hoyer (D-Md.), to thank them and encourage them to vote for the MX again today.

House Republican leaders contacted some Republicans who voted against the missile, including Rep. Christopher H. Smith (R-N.J.), to try to change their votes.

MX opponents would have to switch three votes to defeat the 21 missiles, which they acknowledged would be difficult because, for the first time recently, there were no absences on a vote: Everyone is now on record.

Sources said that MX opponents considered less than a dozen lawmakers to be switch possiblities, including Reps. Wayne Dowdy (D-Miss.), Stephen L. Neal (D-N.C.), Carroll Hubbard Jr. (D-Ky.) and Wes Watkins (D-Okla.).

Common Cause President Fred Wertheimer, a leading MX foe, declined yesterday to specify who the anti-MX groups had targeted but said "we're calling all our people -- or as many as we can reach -- and thanking them for a courageous vote."

O'Neill, House Majority Leader James C. Wright Jr. (D-Tex.) and House Majority Whip Thomas S. Foley (D-Wash.) were all said to be contacting members yesterday. In addition, Sen. John Glenn (D-Ohio) met with a handful of Democrats, both opponents and supporters, to stress the cost of the MX and urge them to defeat the 21 missiles.

While MX opponents were avoiding predictions on today's vote, they were more optimistic on the next MX battle -- the 48 missiles Reagan has requested in his fiscal 1986 budget.

The House vote Tuesday was to authorize 21 missiles.

Today's vote is on whether to appropriate the $1.5 billion needed to produce them. It is the last hurdle to their production. The Senate approved the missiles last week.

But Democratic supporters of the MX, who helped the administration win approval for the MX, have said they will not support the request for 48 and will likely propose scaled back deployment.

"The administration has to realize that Congress is only going to approve 40 to 50 missiles," said one of those Democrats, Rep. Norman D. Dicks (D-Wash.).

In the Senate, three key Democratic backers of the MX, Sam Nunn (D-Ga.), Albert Gore Jr. (D-Tenn.) and Minority Leader Robert C. Byrd (D-W.Va.), are to unveil a proposal today to cap deployment at 40 missiles.

Reagan has argued that more missiles are needed for the renewed arms control talks, to modernize U.S. nuclear forces and to compete militarily with the Soviets.

MX foes contend that the weapon is too costly, too vulnerable and unnecessary to arms control efforts.