With fewer than six weeks remaining before election day, the Republican Party has failed to convince voters that it is any better able than the rival Democratic Party to handle a problem it hoped to turn to its advantage - taxation.

In the latest Gallup Poll, just 25 percent of Americans say the GOP can do a better job of holding down taxes while 31 percent name the Democratic party. Almost half the public, 44 percent, either sees no difference in the ability of the two major parties to handle this issue (33 percent) or is undecided (11 percent).

In fact, the GOP continues to suffer from a serious "issue gap." Not only do voters give the Democrats the benefit of the doubt on this supposedly Republican issue, but they credit the Democratic Party as better able to deal with three other critical questions - reducing federal spending, dealing with inflation and handling relations with the Soviet Union.

With six in 10 Americans naming inflation as the most important problem facing the nation, it would seem a particularly opportune time for the GOP to take advantage of this issue, but if present attitudes hold through election day, this will not be the case.

Currently, 31 percent of Americans say the Democratic party is better able to handle the problem of inflation and only 23 percent give the nod to the Republicans. Another 35 percent see no difference between the parties and 11 percent are undecided.

Another so-called Republican issue - reducing federal spending - is turning out to be nothing of the sort. On this question the Democrats hold a 30-to-23 percent lead. Again, about half the public either perceives no difference in the abilities of the parties or is undecided on the issue.

If anything, the Republicans may be losing some ground on this issue. In a similar survey conducted in March there was virtually no difference in the percentages citing either of the two parties as best able to cut federal spending. At that time 28 percent named the Democrats and 26 percent the Republicans.

Finally, the public also prefers the Democratic Party over the GOP as better able to handle relations with the Soviet Union - the one foreign policy issue that is virtually sure to persist during the coming years.

On this question the Democrats hold a 29-to-22 percent lead, with 33 percent saying there is no difference between the two parties and 16 percent undecided.

This inability to convince voters of its ability to deal with the nation's important problems is, no doubt, a major factor in Gallup Poll surveys showing the GOP will gain few, if any seats in the House this year.

Assuming voter intentions do not change dramatically during the closing weeks of the House of Representatives will likely remain much as it is today - about 2-to-1 Democratic.

The one bright spot for the GOP in the survey is the fact that on all four of the issues tested, political independents (who account for about one-third of the electorate) are either evenly divided in their attitudes (as in the cases of taxation and inflation) or see the Republicans as better able to deal with the problem.