House Democrats, forewarned that President Reagan will make tax simplification an important thrust of his State of the Union address, are sharply divided over the merits of such a plan and whether Reagan will own the issue if they don't move fast.

The Democrats' leading tax-simplifiers, Rep. Richard A. Gephardt (D-Mo.) and Sen. Bill Bradley (D-N.J.), are pressing other members of their party, particularly members of the governing House Ways and Means Committee, to support their simplification bill. They have gone so far as to consider a public-speaking tour around the country later this year.

"We want more than just Bradley and Gephardt standing there saying they're for tax reform before the president says it," a Gephardt aide said. "The fear is that the president is going to use the State of the Union address to transcend the deficit problem with tax reform."

But this sense of urgency is not shared by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). Along with Ways and Means Chairman Dan Rostenkowski (D-Ill.), O'Neill fears that the effects of tax simplification may not have been fully thought through.

"His general position is, wait and see what the president proposes," said Christopher J. Matthews, O'Neill's administrative assistant. "His general approach is to keep his powder dry. The party will decide at the right time, I assume, how they'll protect the average person's interests. This shouldn't be seen as some kind of land rush."

Reagan is expected to embrace tax simplification in his State of the Union address Feb. 6, even if the administration has not decided which portions of the Treasury Department's simplification plan to endorse.

Both the Bradley-Gephardt and the Treasury proposals would cut current individual tax rates and reduce their number to three, while also eliminating most deductions, exemptions and other special tax-reducing provisions now in the code. The top rate for individuals, now 50 percent, would be 30 percent under Bradley-Gephardt and 35 percent in the Treasury plan. There would be a similar trade-off of lower rates for fewer deductions for corporations.

The plans differ in such areas as where on the income scale each bracket would take effect, how they would restructure depreciation write-offs and whether to end indexation of tax brackets to inflation. A third such plan, sponsored by Rep. Jack Kemp (R-N.Y.) and Sen. Robert W. Kasten Jr. (R-Wis.), is also in the running.

Simplification advocates at both ends of Pennsylvania Avenue agree that there will have to be bipartisan negotiations if a plan is to get through Congress. But Democratic sponsors fret that -- if simplification becomes popular with voters, as polls suggest it might -- Reagan will get the credit for what was originally a Democratic idea.

To marshal the troops, Bradley has been meeting regularly with members of the House Ways and Means Committee, "pulling out all the stops," in the words of one committee aide. "He's been working at it real hard. He's trying to sign up the whole damn committee."

The difficulty in lining up the leadership so far reflects not just caution on the part of Democrats after the Reagan landslide last November, observers say, but a division within the party about simplifying the code rather than continuing to use it to further social goals.

"I would say there's some confusion," the Gephardt aide said.

Last summer, for example, supporters of rival presidential candidates Sen. Gary Hart (D-Colo.) and Walter F. Mondale quarreled bitterly over whether to include a reference to Bradley-Gephardt in the party platform (they didn't). And Hart's campaign positions included a call for tax simplification and a host of new tax breaks to increase investment and savings.

"All the Democrats say they like tax simplification. But if you pin them down, there are always two or three parts they don't like," a Senate Democratic aide said. Some Republican members of Congress also have such reservations, and many members doubt that a simplification bill can pass, no matter what stand the Democrats officially take on the issue.