A new, confidential nose count by the House Democratic leadership shows that 60 of the 63 conservative Democrats who "defected" to support the president's budget-cut plan last week will not back a similar bolt on his tax-reduction bill.

The findings of the poll, taken by House Speaker Thomas P. (Tip) O'Neil (D-Mass.), were immediately confirmed by several key members of the conservative Democratic rump group that had joined the Republicans on the budget vote.

The nose count, while not final, added dramatically to already emerging evidence of congressional resistance to the Roth-Kemp tax plan. On Monday, Senate Finance Committee Chairman Bob Dole (R-Kan.) said support for the Reagan proposal now is lukewarm.

Congressional leaders have been contending the White House couldn't muster the kind of support for the tax bill that it enjoyed on the budget resolution, but this is the first hard evidence they've produced. The White House, discounting such claims, has shied away from any compromise.

Administration sources said President Reagan will meet with Democrats on the Senate Finance Committee today to discuss his tax-cut plan but said the session was meant only to sound the legislators out and not to work out any agreement.

The meeting, which officials said was planned several weeks ago, comes as the Finance Committee is scheduled to begin hearings on the Reagan tax-cut proposal, apparently well short of the votes needed to push the bill through intact.

Meanwhile, Democrats on the House Ways and Means Committee are scheduled to hold a strategy caucus this morning in view of the new leadership nose count. Chairman Dan Rostenkowski (D-Ill.) is seeking a unified party position to avert another round of defections.

Today's delegation to the White House, headed by Sen. Russell B. Long (D-La.), ranking minority member of the panel, is intended to give conservative Democrats on the committee a chance to make their views known to Reagan directly.

Officials said there still have been no decision on whether to issue a similar invitation to Rostenkowski. However, several key members of the committee said they'd received indications that such a move was in the works.

Meanwhile, administration officials confirmed that because of newly soaring interest rate, the fiscal 1981 budget now is likely to reach between $60 billion and $62 billion, rather than the $54.9 billion previously expected.

However, acting White House press secretary Larry Speakes promptly blamed the Carter administration for the large red-ink figure. "We are dealing with an economic situation that we inherited," he said. "We're simply forced to do the best we can."

The nose count of the 63 one-time defectors is important.Conservative Democrats in the House had been expected to draft their own tax-cut proposal, as they did in the fight over the budget resolution, but so far they've been holding back pending discussions with Rostenkowski.

House strategists said the Southerners' opposition to Roth-Kemp goes beyond merely the full three-year bill. Sources said only 10 of the Southerners polled even were willing to vote for a two-year version of the Reagan bill. Their main concern is that it would bloat the budget deficit.

The remainder was said generally to support a Democratic alternative proposed by Rostenkowski, which would provide a much smaller one-year cut, skewed more to benefit low- and middle-income taxpayers.

The measure proposed by the president, based on a plan by Rep. Jack Kemp (R-N.Y.) and Sen. William V. Roth (R-Del.), would provide for a 10 percent across-the-board cut in federal income tax rates for each of three years.

Sources said the Ways and Means chairman has been applying firm pressure on individual members in an attempt to avert the kind of intraparty blood bath that occurred over the budget measure.

Meanwhile, at least one mainstream Democrat on the panel, Rep. Richard Gephardt (D-Mo.), has served notice to colleagues that he will oppose a tax cut of any size -- on grounds that it would only enlarge the expected budget deficit and exacerbate inflation.

Gephardt cited fears by the financial markets that the increased deficit would raise interest rates further. Aides said the congressman's constituent mail has stressed cutting the budget but hardly has mentioned a tax reduction.

The support of the Finance Committee Democrats is crucial to ultimate approval of the Reagan tax-cut plan, even though the Senate is dominated by Republicans. Several GOP members of the committee, including Dole, are lukewarm about the Roth-Kemp plan.

Administration sources said besides Long, the Finance Committee Democrats invited to the White House today include Sen. Lloyd Bentsen of Texas and Sen. David L. Boren of Oklahoma. Other names were not available late yesterday.