As Congressional leaders met on Tuesday with President Bush to continue hashing out the parameters of an economic stimulus package — and indicated that the House will lead debate on the measure — some rank-and-file lawmakers began hinting that they’d like a more active role in the negotiations.

“We’re here today because we have an urgent matter to deal with,” Speaker Nancy Pelosi (D-Calif.) said Tuesday morning, before leaders from both parties met with Treasury Secretary Henry Paulson. “We’re going to work in a bipartisan way and with the president to do just that.”

Senate Majority Leader Harry Reid (D-Nev.) indicated the stimulus measure still is on a fast-track schedule, targeting its completion before the President’s Day recess begins Feb. 15, just a few weeks away.

“We need to have something on the president’s desk by then,” Reid said.

After meeting with the president on Tuesday, Reid said that he and Senate Minority Leader Mitch McConnell (R-Ky.) would wait for the House to act. However, Reid appeared to warn Pelosi and House Minority Leader John Boehner (R-Ohio) of the imperative for the House to pass something that would garner wide support in the Senate, given that 41 Senators can filibuster a bill.

“Sen. McConnell and I … legislatively, have a little more difficult time doing things,” Reid said. “But we think it would send a tremendous message to the American people that we have something bipartisan that comes to us from the House, and we’ll do everything we can, in the Senate, to move it as quickly as possible.”

Nonetheless, Reid remained cautious about negotiations with the White House. Asked if he had changed his opinion that Bush is the most difficult president he’s ever had to deal with, Reid said, “Hope springs eternal. I hope this year that he’ll be a uniter, not a divider. If that happens, we’ll have to wait and see.”

One senior Senate Democratic aide said the key points Reid and Pelosi attempted to make at the White House on Tuesday were: They want a stimulus package that includes spending as well as tax cuts, and they want to make sure as many people as possible receive tax rebate checks.

The aide said Democrats are “determined” to broaden the impact of the rebate checks to people beyond just income tax payers.

“We need to do something that’s simple, something everyone can understand,” Hoyer said of the rebate proposals in a Tuesday press conference.

Bush and Republicans have said people who don’t pay income taxes should not be given government handouts. However, the Democratic aide said Democrats’ preference to provide the rebate to all payroll tax payers — which would include lower-income families — was up for negotiation.

The topic could become a sticking point in the negotiations for House Republicans, Boehner acknowledged. “Ms. Pelosi and I expect we’ll have a vigorous argument on that issue,” he said.

House and Senate leaders expected to continue negotiations over the proposed stimulus package Tuesday evening and into Wednesday. However, the House will not meet Thursday and Friday in order to accommodate the GOP Conference’s retreat. Lawmakers face a similarly short schedule next week when Democrats are scheduled to hold their own retreat.

In the meantime, rank-and-file lawmakers on both sides of the Capitol have begun to tout their own economic fixes — both short- and long-range — as it remains unclear whether Members will be given any opportunities to shape the legislation.

The conservative Republican Study Committee will unveil its Economic Growth Act today — targeting business growth with reductions in the corporate tax rate as well as restructuring capital gains taxes — while the Congressional Black Caucus has called for increased funding to boost an existing “summer jobs” training programs, as well as tax breaks for small businesses.

Members of the New Democrat Coalition have also begun lobbying House leadership to include investment tax credits and accelerated depreciation measures.

“They won’t be offering something that’s stand-alone because they want to work with leadership on it,” said NDC spokesman Kevin Lawlor.

A senior House aide, who asked not to be identified, asserted that Democrats have sought out rank-and-file Members on the stimulus plans — focusing Democratic Caucus meetings on the subject two weeks running and meeting with senior lawmakers.

“Leadership is aware of different [factions] in the Caucus and their ideas,” the aide said.

While a Republican aide, who also asked not to be named, said there has not been significant discussion with rank-and-file Members — “leadership has been going to the president and to the Democrats,” the aide said — he acknowledged that those conversations are expected at this week’s retreat at the Greenbrier Resort in West Virginia.

On the Senate side, individual lawmakers on both sides of the aisle sought to inject themselves into the debate by issuing press releases on their preferred economic stimuli. For example, House Small Business ranking member Olympia Snowe (R-Maine) pressed for tax incentives that would allow small businesses to invest in more equipment, while Sen. Tom Harkin (D-Iowa) advocated for a stimulus that would “put Americans to work to repair our schools and rebuild our public facilities and infrastructure.”

Plus, two influential GOP Senators expressed skepticism about the usefulness of an economic stimulus bill.

Budget ranking member Judd Gregg (R-N.H.), who also serves as an unofficial McConnell adviser, told reporters he was trying to raise a “red flag of reason” to prevent Congress from passing an economic stimulus that would saddle future generations with debt or dip into the Social Security trust fund in order to provide rebate checks to Americans.

“We’ll see if anyone listens,” said Gregg, who nevertheless said he is resigned to the fact that legislation is all but certain to pass Congress in the next month or so.

“It appears to be this train is going to leave the station,” Gregg said. “It’s not moving in a fiscally responsible way, I’m afraid, but it’s moving.” Gregg said the expedited process was more about both parties trying to win this year’s election than it was about responding to an economic crisis.

Referencing the country’s reliance on cheap goods from China, Gregg also questioned who would benefit from any rebate checks. “Are you going to be energizing the American economy or the Chinese economy?” Gregg asked.

Meanwhile, Senate Finance ranking member Chuck Grassley (R-Iowa) also raised concerns about the need for a stimulus package, but he too acknowledged that “the fiscal stimulus horse has left the barn.”

“With the die cast that we need some kind of fiscal stimulus, again, how do we best respond to the immediate situation and not damage economic growth over the long term?” Grassley asked at a Finance hearing on the economy Tuesday morning.

But Senate GOP Conference Vice Chairman John Cornyn (Texas) said Senate GOP leaders were largely waiting for the White House to give them more specificity about the administration’s proposal before outlining their own preferences. Paulson is expected to address the Conference today at a previously scheduled party retreat at the Library of Congress, he said.