As the off-year congressional election campaign moves into its final week, Republicans appear to have gained the initiative on the issue of federal spending. They now have a 38 to 31 percent edge over the Democrats as the party whose candidates can do a better job of cutting spending.

Republicans have also began to cut into the sizable Democrat lead on the question of which party can better "give some relief to taxpayers." The Democrats still have a 39 to 30 percent edge on this crucial tax issue but, last month it was 42 to 26 percent.

The GOP has been trying to rectify an obvious mistake earlier in the campaign when it emphasized passage of the Kemp-Roth bill, which would slash federal taxes by 33 percent over a three-year period which did not call for commensurate spending cuts. The reaction of most voters was outright skepticism.

On this year's dominant issue of who can do a better job of inflation control, the Democrats cling to a narrow 33 to 32 percent edge. Thus, on two of the three top issues, all centering on the economic plight of the country, the Democrats hold a slight lead but are now on the defensive as the campaign enters its final week.

On two other issues tested in the latest Harris-ABC Survey of 1,200 voters nationwide, the GOP holds a widening edge:

On "keeping the military strength of the United States at least as strong as the Russians," the Republicans are now preferred over the Democrats, 37 to 31 percent, up from a 34 to 34 standoff just last month.

On "supporting stronger measures to control crime," the Republicans are ahead by a close 32 to 29 percent, a turnaround from the September results showing the Democrats ahead, 33 to 29.

However, on four other issues, the Democrats hold a substantial lead:

On "helping the elderly and the poor get a better break," on "achieving peace in the Middle East," on "backing a SALT agreement with Russian to control nuclear weapons," and on "passing a comprehensive national insurance bill."