A full 13 months before his next election day, Arizona Gov. Bruce Babbitt devoted most of a perfect Saturday morning to campaigning in Cochise County. That same afternoon, he rededicated the original London Bridge, another transplant to Arizona, at its new location in Lake Havasu City.

Babbitt, a 43-year-old Democrat whom the 1982 "Almanac of American Politics" calls "one of the nation's brightest and most thoughtful governors," is obviously running hard for re- election. For any incumbent in these political times, running hard, early, makes good sense; for an incumbent Democrat in Arizona, there is no rational alternative.

The voters of Arizona and the 10 other mountain and Pacific western states do not like national Democrats, of whom Bruce Babbitt is most definitely one. And that regional dislike seems to be growing.

Take the presidential votes. Just like George McGovern in 1972, Jimmy Carter in 1980 lost all 11 of the western states. But while McGovern averaged 36 percent of the vote in those states, not too far off his national showing, Carter could average only 31 percent in the same states, running behind McGovern's percentage in every one of them.

Arizona is, by presidential voting, the most Republican state in the union. No Democrat since Harry Truman has carried its electoral votes. Every other state since then has voted Democratic at least once. The 1980 returns from the Grand Canyon State were more of the same, only more so: Reagan-Bush, 61 percent of the vote; Carter-Mondale 28 percent and Anderson-Lucey 9 percent.

According to recent candidate polls in the state, the president's popularity, is not only undiminished, but by some readings even increased from over a year ago.

But the Republican president's popularity does not inhibit the Democratic governor from criticizing publicly and persistently the Reagan philosophy and programs. Charging that the administration has "repeatedly proclaimed what it should not do," Babbitt argues that the president "has given no public thought to what is and what is not a federal responsibility."

Bruce Babbitt has some definite ideas about what should be federal responsibilities and his own three-question examination to determine which public activities should be handled by the feds and which by the locals.

Here is the Babbitt litmus test for federal or non-federal responsibility:

Where traditionally has the public activity been performed, locally or federally? What is the current degree of federal financing of the public activity? And, third, would federal divestiture of the public activity lead to negative and unhealthy competition among the states?

By this test, Babbitt believes that the federal government should end all aid to and financing of the arts, local law enforcement, elementary and secondary education, as well as highways and mass transportation.

The federal government, according to the Babbitt test's author, has the first responsibility for providing economic security to the nation's citizens. In addition to the federal role in Social Security, this would also mean the assumption by the federal government of the cost of welfare and individual health programs.

Babbitt believes that under the existing system, "for the states that meet their responsibilities in welfare and air pollution, their short-term benefits are so slight that other states can compete negatively, lowering standards and benefits." It may be unorthodox, but it is interesting.

Some of Babbitt's criticism is reserved for his own party, which he has faithfully supported. He sees Democrats as "undisciplined, incapable of making choices and asserting priorities." He told a California Democratic dinner last June, that the "egalitarian principles of our own party demand . . . and the quality of our military effort requires" that we abandon the volunteer army and reinstate the draft. Babbitt can now smile at how quiet the Los Angeles crowd became with that proposal. But Babbitt clearly is convinced that Reagan has, as he puts it, "oversold weaponry as cure for our national defense woes."

The Democrats are accused of having run out of ideas, of letting their programs become values unto themselves and the Democratic values harden into Democratic theology. Bruce Babbitt has some different ideas, and before long we may find out whether other Democrats are listening.