By putting his office publicly on the line last weekend, West German Chancellor Helmut Schmidt has placed himself out on a political limb on which he could well be left hanging for a considerable time.

Long heard to grumble to his friends and in closed party circles about how he might quit his office prematurely for a less hassled life, Schmidt went public this week in a speech to members of his Social Democratic Party with an implicit threat to resign if some in the party did not stop sniping at NATO plans to station new medium-range nuclear missiles in Europe.

In one bold step, he has challenged the left wing of the party and President Reagan, from whom he may hope to gain stronger commitments to resume negotiations toward limiting nuclear missiles in Europe during his visit to Washington beginning Wednesday. The weekend statement caught his left-wing party critics -- and nearly everyone else -- by surprise and has managed to lend Schmidt, after months of appearing to duck a messy intraparty clash, the renewed image of a warrior chancellor.

By clearly staking his continued leadership on his party's unwavering support for the NATO missiles decision, Schmidt sent a signal to Washington of what he would stake on keeping to the alliance course, perhaps in hopes that by taking such a tough stance domestically, the Reagan administration would be moved to futher commitemnts to resume the missile talks.

A Bonn government source was quoted today by the Deutsche Presse Agentur as saying it would be Schmidt's aim to encourage the Reagan administration, which has promised the resumption of arms talks with Moscow before the end of the year, to move up the starting date to early autumn and to deliver a more precise public statement about Washington's desire to negotiate seriously. If the chancellor can achieve this, the government source said, then his trip could be called successful.

The daily Frankfurter Allgemeine Zeitung suggested today that Schmidt's threat to resign simply may have been a sign that he has had enough of trying to show tolerance for left-wing positions on security policy and that he possibly acted partly our of impatience.

The Social Democart's national convention, at which party support for the NATO decision will be reviewed, is not until next spring, and there are another 2 1/2 years to go before the new U.S.-made Pershing II and cruise missiles approved by NATO in December 1979 are due for deployment in Europe.

"Schmidt has accepted the challenge and could end it in his favor soon," the Hamburg daily Die Welt wrote. "Bu if the entire matter is deferred until next April, then he has drawn his sword prematurely and, thus, in vain. Time apparently is working against Schmidt's policy."

As though preparing a scorecard for a lenghty political sporting match ahead, the mass-circulation daily, Bild-Zeitung, today carried on its front page the faces of six of Schmidt's most outspoken critics in his party under the headline: "Will these men bring down Schmidt?"

Implicit in Schmidt's gamble seems to be the assumption that once the Reagan administration apprecaites how much at risk Schmidt and his government are on the NATO missile issue, it will toss the West German leader a support line in the form of serious and urgent negotiations with the Soviet Union to limit the number of nuclear warheads in Europe.

The United States pledged to pursue such talks as part of the original missiles decision. What looks to the Social Democratic left wing as foot dragging by the Reagan administration on this pledge has contributed largely to current West German political pressures on Schmidt to review the missile deployment plans.

It would be natural at this point however, for Washington to be considering the consequences of a change in government in Bonn that would allow the conservative Christian Democrats, traditionally more pro-American than the Social Democrats, to return to power.

The question is whether Reagan -- and Soviet President Leonid Brezhnev, who is scheduled to see Schmidt in Bonn later this year will decide to do whatever may be necessary to adjust their own plans for superpower negotiations in order to accommodate Schmidt and allow the West German leader to climb back on top, or at least serve out his term.

In raising his challenge to his party's left, Schmidt seems to have left himself at the mercy of the two superpowers. If they are unable to bail him out, his domestic difficulties could prove his undoing.