The House Rules Committee voted yesterday to head off a Republican bid for a House vote on the party's tax-cut proposal but then stumbled over a breakdown in Democratic discipline on the committee.

As a result, the committee put off action on a $10 billion package of congressional spending cuts and revenueraising measures that had been scheduled to go to the House floor for action today.

The committe had no trouble disposing of the tax-cut proposal offered by Rep. Baarber Conable (R-N.Y.) -- a 10 percent cut in proposal incomed tax rates and business tax cuts that Republican presidential nominee Ronald Reagan is advocatin for 1981.

By voice vote, the Democratic majority on the committee rejected Conable's proposal to permit a vote on the tax cut in conjunction with a vote on the so-called budget reconciliation package. It also defeated a proposal by House GOP Whip Robert H. Michel (R-Ill.) to allow a vote on another Republican proposal to authorzie the president to impound funds that exceed budget ceilings.

The Senate has rejected the Republican tax-cut proposal a couple of times, but it has not come to a vote on the House floor since it emerged as an issue in the presidential campaign.

Things began to fall apart when Rep. Robert E. Bauman (R-Md, acting on a proposal advanced earlier by Rep. Joseph L. Fisher (D-Va.), proposed a floor vote on a provision in the package that calls for annual -- rather than the current semiannual -- cost-of-living adjustments in the pensions of federal workers. The change had been proposed to save roughly $700 million in military and civilian pensions during the next fiscal year.

Three Democrats -- Reps. Shirley Chisholm (N.Y.), Joe Moakley (Mass.) and Leo C. Zeferetti (N.Y.) -- jumped party traces to vote with the Republicans on Bauman's proposal, and it passed, 8-7.

At this point, Rules Committee Chairman Richard Bolling (D-Mo.) suspended the meeting in hopes of reversing the vote, a process that sources said may have to entail some persuasion from House Speaker Thomas P. O'Neill (D-Mass.).

House Democratic leaders fear that the political strains of floor amendments could shatter the fragile reconciliation package, which was a key part of earlier efforts to put together a balanced budget and is now viewed as critical to keeping the newly projected $30 billion deficit for 1981 from going even higher.

"If anyone wants to nitpick this, then they can nitpick it to death," warned House Budget Committee Chairman Robert N. Giaimo (D-Conn.).

Meanwhile, big business and big labor staked out separated positions before the House Ways and Means Committee on the need for quick enactment of tax-cut legislation, Associated Press reported.

AFL-CIO President Lane Kirkland said a proposal by Republican presidential nominee Ronald Reagan and his congressional supporters "amounts to a subsidy for the business community through the back door."

But Theodore Brophy, chairman of General Telephone & Electronics Corp., said a tax cut "is urgently needed now to set the stage for healthy long-term economic growth through the 1980s."

Speaking on behalf of the Business Roundtable, a business group made up of the heads of the nation's largest corporations, Brophy added, "A tax reduction on the order of $30 billion appears not only reasonable, but a necessary first step to improve productivity on a long-term basis."