A few weeks ago, I jokingly suggested in a column that Vice President George Bush select Edwin Meese III as his running mate for the Republican presidential ticket. By picking the attorney general, I wrote, Bush would put the sleaze factor squarely in his column and lock up the general election.

That column was meant to be humorous, but the idea of Bush picking an attorney general as his running mate is still a good one. It's just that the man for the job isn't Meese, it's Richard L. Thornburgh.

The director of the Kennedy School's Institute of Politics (IOP) and the former governor of Pennsylvania was nominated last month to replace the departing Meese as the head of the Justice Department. He had been mentioned as a possible running mate before his nomination, but since then his name has been largely ignored when political observers discuss the GOP ticket.

Although Thornburgh will be very busy getting confirmed as attorney general by the Senate and cleaning up the mess left in the Justice Department by Meese, this should not exclude him from consideration for vice president. The IOP director offers the Republican Party a great opportunity to highlight its differences with Gov. Michael S. Dukakis as well as get some free publicity at the expense of Democratic Party.

THE Senate confirmation hearings on Thornburgh begin today and will give him a great chance to make headlines and garner praise from Republicans and Democrats alike. Already, Thornburgh has been praised by many Democratic leaders as a qualified public servant with a great reputation for personal integrity. He is expected to pass through the Senate hearings with as little trouble as a hot knife has passing through butter.

Sen. Edward M. Kennedy '54 (D-Ma.), who will chair the hearings today because of an illness to Judiciary Committee Chairman Sen. Joseph Biden (D-Del.), said at the time of the nomination's announcement that he had the "greatest respect" for Thornburgh, adding that "the state of justice in America would be very different today if Dick Thornburgh had been attorney general for the past three and a half years instead of Ed Meese."

If Thornburgh were named as the vice presidential running mate after the hearings, there is no way that Kennedy, or any of the other Democrats who will praise Thornburgh during the appointment hearings, could criticize him as incompetent or lacking integrity.

Sen. Patrick J. Leahy (D-Vt.) also praised Thornburgh at the time of his appointment, calling him a "man of competence." Competence is the main theme of the Democratic presidential candidate's campaign. Completing the Republican ticket with a "man of competence," would easily deflate the Democratic balloon.

The effect of Bush selecting Thornburgh as his running mate, would be to nullify one of the main criticisms weighing down his campaign--the Reagan Republican sleaze factor. Today, Thornburgh will be widely praised as a man of great personal integrity by the Senate leaders, many of whom will also take the opportunity to criticize the indiscretions of Meese. In choosing Thornburgh--the antithesis of Meese--Bush can project an image of a cleaner and more honest administration.

THORNBURGH will also be praised today for being a moderate rather than an ideologue. He is a Republican in the tradition of Rockefeller and Howard Baker, two men coming from the more widely respected wing of the party. To many moderates, including moderate Democrats who voted for Reagan in 1980 and '84, the choice will appear to indicate that a Bush administration will be more in the mainstream than the Reagan administration has been.

In fact, the loudest opposition to Thornburgh may come from some of those furthest to the right. Sen. Gordon Humphrey (R-N.H.), a staunch supporter of the pro-life movement, raised a number of questions about Thornburgh's stance on the issue of abortion.

But while a less unforgiving position on this issue may attract moderate Democrats, even this will not split the Republicans. Even if Thornburgh's and Bush's records of support for the pro-life movement are not as strong as the records of Orrin Hatch and Henry Hyde, they are far closer to the right than the records of Dukakis and Sen. Lloyd M. Bentsen (D-Tex.) The real pro-lifers, the great majority of whom vote, will surely not turn to the Democrats.

Geographically, the selection of Thornburgh creates a problem for the Republicans, but not a great one. It may even prove strategic. By selecting a Northeasterner, Bush can go whole hog in pretending to be a Texan which he will need to do to beat Bentsen in the Longhorn State. And with Thornburgh on the ticket, such a move won't mean sacrificing support in the Northeast and Middle Atlantic states.

Thornburgh also can guarantee the Republicans a state with a large number of electoral votes. Pennsylvania and it's 25 votes, which went for Reagan in 1980 and '84, has to go for the Republicans in 1988 for Bush to win.

Thornburgh served for the maximum two consecutive terms in the state from 1979 to 1987 and earned high performance ratings from just about everyone. When he left office, he still had a public approval rating of 72 percent.

THE similarities between Bush and Thornburgh will also help the Republicans play up the ideological differences between Bentsen and Dukakis on the Democratic ticket. Bush has spent much of his time criticizing Dukakis as weak on crime. Thornburgh's record as a hard-nosed crime buster when he was governor of Pennsylvania and as the head of the criminal division of the Justice Department will help to show the Democrats as weak on crime.

Bush needs to overcome the so-called convention bump that has propelled Dukakis to big leads in opinion polls following the Democrat's party in Atlanta. The Bay State Governor's lead will shrink over the next few weeks, especially after Bush has a convention of his own in to put him in the spotlight.

What Bush needs to do to bounce back himself is select a running mate who possesses the best characteristics of the Republican party with few of its drawbacks. Thornburgh fits the description.