With Democratic National Committee Chairman Paul G. Kirk Jr. urging his party "to put our rules fights behind us," the 378-member DNC appeared headed for quick and easy ratification today of a set of rules for the 1988 presidential selection process that will be only slightly different from those used in 1984.

Last night, the only potential source of a major floor fight over the rules evaporated as the DNC Black Caucus approved a compromise resolution that calls for the elimination of thresholds -- minimum votes a candidate must receive in order to be awarded delegates -- but endorsed the recommendations of the party's Fairness Commission, which include a 15 percent threshold for 1988.

As Kirk pitched the rules proposed by the Fairness Commission at four regional DNC caucuses yesterday, he also said critics of a move to create a "super-duper Tuesday" of primaries and caucuses in early March were sounding a "false alarm" and questioned whether all states talking about moving their dates would actually do so.

However, the sentiment among southerners for an early regional primary appeared to solidify yesterday. "When you get bit four or five times by the same dog, you get a new dog," Texas Chairman Robert Slagle said in explaining the shift, which has quickly become the rallying cry of the region.

The movement toward "frontloading," holding primaries early in the political season, is expanding beyond the South. New Jersey Democrats, with the encouragement of Republican Gov. Thomas Kean, said they are considering moving their primary from early June to March 8, and California Democrats have apppointed a commission to consider whether to move its primary back from its traditional early June date. California Chairman Betty Smith said the state feels "neglected" because it sets at the end of the calendar.

On the other hand, at least one state that currently holds its caucus in mid-March, Michigan, will consider moving to April so it will not get lost in the March rush, Chairman Rick Wiener said.

Meantime, as the calendar jockeys spun their various strategies and scenarios, Fairness Commission Chairman Donald Fowler outlined what he called four "perfecting amendments" to the 1984 party rules that he will ask the DNC to approve today. They are:

*Open Primary. Historically, Democratic primaries and caucuses have been open only to voters who declare themselves Democrats. This closed rule will remain in force, but an amendment for 1988 will permit open primaries in states -- Wisconsin and Montana, for example -- where a nonpartisan political tradition is inconsistent with a declaration of party preference.

*Timing. The 13-week "window" in which states must hold their primaries or caucuses, from early March to early June, will remain in place, but four states will be granted exemptions so they can hold their contests before the window opens: Iowa, New Hampshire, Maine and Wyoming. Fowler noted that the DNC had tried to bring those states into the window in 1984 and "we broke our pick . . . . This ratifies the inevitable."

*Thresholds. In 1984, the party established a 20 percent threshold as part of a series of "winner-take-more" rules designed to help front-runners sew up the nomination. Now the commission is proposing that the threshold be cut to 15 percent. The Rev. Jesse L. Jackson has complained that the threshold cost him hundreds of national convention delegates in 1984. Former Atlanta mayor Maynard Jackson said last night that thresholds discriminate against all candidates who do not have a broad electoral base; Fowler responded that thresholds are necessary to avert the specter of a brokered convention.

*Superdelegates. In 1984, the DNC reserved 14.3 percent of its national convention slots to "superdelegates," party leaders and elected officials who went to the convention unpledged. The idea was to give leaders more of a role in the process. For 1988, the commission proposed that the superdelegate slots be expanded slightly, to 15.5 percent, and that they be composed of all Democratic National Committee members, all Democratic governors, and four-fifths of all Democratic U.S. House and Senate members. The commission also calls for the House and Senate members to be chosen in late April, rather than in late January, as they were in 1984.

On another matter, Houston got a jump on the field of cities interested in hosting the 1988 Democratic National Convention yesterday as Mayor Kathy Whitmire threw a reception and distributed a glossy brochure touting a convention center that will be completed next year.

The DNC site selection committee, chaired by Bethesda real estate developer Nathan Landow, is expected to choose a city by the end of this year. So far, Houston, Atlanta, Philadelphia, San Diego, Orlando, Kansas City, the District of Columbia, Chicago, Los Angeles and Cleveland have indicated an interest.

Also, Kirk nominated C. Victor Raiser II of Washington to be the party's national finance chair and he announced a $1.2 million program to send 32 fund-raising consultants and campaign staff workers to 16 states to help state parties raise money and build computerized voter files.