The congressional debate over two key tax issues--the 10 percent rate cut scheduled for July 1 and indexation--has torn traditional partisan and ideological alliances, putting some of the most liberal House Democrats in the same camp as President Reagan and splitting the Senate's Republican majority.

The conservative Heritage Foundation is calling for full retention of the rate cut in order "to shift the tax burden to the rich."

At the same time, many populist-minded freshmen Democrats seeking to affirm their opposition to the Reagan tax program have formed a de facto alliance with corporate lobbyists seeking to protect business tax breaks to try to kill the rate cut.

Similarly, on the House Ways and Means Committee, one of the leading proponents of indexation is Rep. James M. Shannon (D-Mass.), a liberal whose one "problem" is that "the president has taken the same position" he has.

For many Democrats who share the goal of continued support of domestic spending programs, the tax issue has been particularly divisive.

Some Democrats argue that repeal or postponement of indexation and the rate cut is essential to restore the federal government's revenue base, and that retention of indexing will make permanent what they see as an inequitable tax burden.

Others counter that killing these tax breaks will intensify the decline in middle-class support for domestic spending, making such programs as welfare and food stamps all the more vulnerable, while retention of the tax reductions will create pressure to close loopholes benefiting those in the upper brackets.

Congress forced itself to focus on the issue when the House approved a $30 billion tax increase earlier this year and the Senate Budget Committee did the same. Members on both sides expect the full Senate to approve a lower figure, however.

The murkiness of the tax debate is rooted in the Reagan administration's $749 billion 1981 tax bill.

It proved on the one hand to be a substantive victory for conservatives, who won a massive reduction in federal revenues with benefits going to the affluent, and on the other to be a political bonanza for Democrats, who revived the charge that the GOP is the party of the rich.

But, as Democrats and some Senate Republicans began to look for ways to correct what they see as an unjust tax program, they have encountered a political reality: it is much harder to take away an existing tax break than to postpone or repeal a prospective tax break.

The provisions in the 1981 bill that benefit the wealthy include reducing the top tax rate from 70 to 50 percent and the maximum capital gains rate from 28 to 20 percent, a $75,000 exclusion on foreign income, a reduction in the estate tax, expansion of retirement savings tax breaks and dividend reinvestment breaks.

The remaining major provisions in the tax bill that have not gone into effect are the third stage of the individual tax cut, scheduled for July 1, and annual indexation of tax rates to changes in the Consumer Price Index scheduled to start in 1985.

The cost to the federal government of the rate cut is estimated at $28 billion in 1984 and the cost of indexing is estimated at $17 billion by 1986. Attacks on these two provisions, however, have ambiguous political consequences.

Repeal of the rate cut would hurt least those in the highest brackets.

For all but the very richest taxpayers, the July rate cut will provide from 35 to 38 percent of the total benefits they will realize from the 1981 bill. For those making more than $200,000 annually who already have reaped the benefits of other provisions, repeal of the cut would mean the loss of only 13.4 percent of their total tax reduction, according to the Joint Taxation Committee.

Because of this, House Democrats are likely to abandon any serious effort to seek full repeal, and, instead, try to cap the benefits of the July cut so that no taxpayer would get a larger break than $700.

Such a move would raise $6 billion in additional revenues in 1984 and would retain the full benefits for all taxpayers filing joint returns with incomes up to $42,500. House Republicans, however, are trying to marshal enough votes to sustain a veto of capping legislation.

Indexing presents a more subtle problem. It is designed to counter inflation, which has a regressive effect on the tax system. Inflation hurts most those with low incomes, and erodes the value of the personal exemption and the standard deduction, which are most valuable to those of less than median income.

At the same time, however, indexation would restrict future attempts to alter the distribution of the tax burden in any direction.

The experience with indexation at the state level has produced conflicting claims. Proponents contend that it has increased public support for the tax system, while opponents contend that it has limited government's ability to respond to needs for additional revenues.