NEW YORK (CNN/Money) - The influential chairman of the Senate Finance Committee will present a tax plan to Senate Republicans Monday night that doesn't include a dividend tax cut, CNN has learned, the latest sign President Bush's hopes for such a plan are fading fast.

Sen. Charles Grassley, R-Iowa, the Finance Committee chairman, will present a package that includes much of what Bush wants, including accelerating the reduction of tax rates, a child credit, the elimination of the marriage penalty and incentives for business investment, according to a top aide to Senate Majority Leader Bill Frist.

However, Grassley will leave the most contentious issue, the dividend cut, for the Finance Committee to resolve when it takes up the bill on Thursday, according to the aide.

"It will not include the dividend because we still haven't been able to work it out," the aide said. "What he [Grassley] will lay out will not be the full $350 billion tax proposal because what he'll say is that there are some holes to work out."

A Wall Street Journal report Monday said Republicans -- reluctant to deprive Bush of one of his top domestic priorities -- could try to add a gradual dividend-tax repeal once the Finance Committee begins debating the bill.

The 2004 budget caps the Senate package at $350 billion, and the immediate dividend-tax repeal that Bush wants would cost about $400 billion.

One option being explored would be to phase in dividend tax relief for investors, which Senate Majority Leader Bill Frist said could cost as little as $70 billion over five years, the Journal reported.

But Grassley is unenthusiastic about that approach, judging it to be shoddy tax policy, the Journal report said, quoting people close to the senator.

And several key moderate Republicans remain skeptical of the prospects for a dividend tax cut to pass the committee. An aide to committee member Olympia Snowe of Maine told CNN she is "cool" to proposals to phase in the dividend tax cut.

Along with Ohio Republican George Voinovich, Snowe persuaded Grassley to hold the total tax package to $350 billion earlier this month, and only go beyond that figure if money could be found elsewhere in the form of offsets.

Asked how much offset money Snowe believes is actually out there, her aide cited reports from other committees claiming that anything from $35 billion to $53 billion can be recovered by closing corporate loopholes.

Another key GOP moderate, Susan Collins of Maine, told CNN she is unlikely to vote for any tax package that does not include substantial aid to the states. Collins, Republican Gordon Smith of Oregon and Democrats Ben Nelson of Nebraska and Jay Rockefeller of West Virginia are asking for $30 billion to be devoted to direct aid to the states, much of it for Medicaid.

"This is extremely important to me, and I'll be back with this issue in determining how I should vote," Collins said.

Like Bush, Collins supports a tax cut of at least $550 billion. But even with the extra money, she thinks a dividend cut is a stretch. "I'm not sure it belongs in this package, and its cost, if you're going to stay within the 550, is problematic," she said.

Separately, the Journal reported Monday that Treasury Secretary John Snow has had trouble winning over people on Capitol Hill to support Bush's tax cut proposals. It noted that Bush selected Snow in large part because of his reputation as a strong salesman with many influential contacts among lawmakers in Washington.  

-- CNN's Jonathan Karl contributed to this report.