An angry warning by President Barack Obama delivered well over a year ago foreshadowed his campaign-style approach on Wednesday aimed at pressuring Republicans to compromise and reach a deal to avoid the fiscal cliff.

In remarks at the White House, Obama urged Americans to call, e-mail and tweet their members of Congress to urge immediate passage of his proposal to extend tax cuts for most Americans while allowing rates on the wealthiest 2% to increase to 1990s levels.

"Let's begin our work with where we agree," the president said, noting the Senate has passed the measure and that both parties agree on holding down rates for the majority of taxpayers. "If we can get a few House Republicans to agree as well, I'll sign this bill as soon as the House sends it my way."

To applause from the White House audience that included those described by organizers as middle-class Americans, the president held up a pen to demonstrate his willingness to sign the law as soon as it reaches his desk.

Meanwhile, a rift among House Republicans on whether to give Obama what the wants became public Wednesday, with two conservatives saying the tax proposal would likely pass if brought to a vote.

House Speaker John Boehner immediately shot down the call by veteran Rep. Tom Cole of Oklahoma for the chamber to approve the Senate measure, saying he disagreed with his colleague. House GOP aides insisted there was no plan to bring the proposal up for a vote.

However, the public call by Cole -- which echoed similar statements from conservatives in recent weeks -- as well as his prediction that the Senate proposal would pass in the House showed an increasing desire among House Republicans to move beyond an issue that has harmed them.

Conservative Rep. Tim Scott of South Carolina also said he thought the Obama tax plan would pass the House, though he made clear to CNN he would oppose it.

The political maneuvering comes as Obama and Congress negotiate a possible agreement to avoid tax increases and deep spending cuts set to take effect in five weeks -- the fiscal cliff scenario that analysts fear could push the country back into recession.

Obama also wants any deal reached in the current lame-duck session of Congress to include an increase in the federal debt ceiling, which is expected to be needed as soon as February or March.

On Thursday, Treasury Secretary Tim Geithner and Rob Nabors, Obama's director of legislative affairs, will meet separately with congressional leaders of both parties, aides said. Geithner is the administration's point man in the negotiations.

Republican rejection of any kind of increase in taxes has been a major contributor to the inability of Obama and Congress to work out a comprehensive agreement in the past two years to reduce the nation's chronic federal deficits and debt.

Obama, who demands some increased tax revenue as part of what he calls a balanced approach with spending cuts and entitlement reforms, became so exasperated at one point during the endless budget battles that he decided to take his argument to the American people.

In July 2011, Obama told House Majority Leader Eric Cantor, one of the lead Republican negotiators, that it was time to make a deal or face the consequences.

"Don't call my bluff," the president said in ending the White House meeting, according to Cantor. "I'm going to the American people with this."

Obama subsequently held a series of events around the country, mostly in swing states for the November election, in which he pushed for higher taxes on the wealthy as part of his main campaign theme to restore equal opportunity for the middle class.

Re-elected and facing the same fiscal issues -- a seemingly unbridgeable divide with Republicans over taxes and spending -- Obama is again taking his case to the people this week.

"The lesson is that when enough people get involved, we have a pretty good track record of making Congress work," Obama said Wednesday.

Cole and some other conservatives say such pressure is the reason to simply give the president what he wants and move past the immediate tax issue.

"If we agree that taxes shouldn't go up on 98% of the people, shouldn't we take that now and get that set aside and make sure they know their taxes aren't going up?" Cole said Wednesday night on CNN's "Anderson Cooper 360."

Sounding a lot like Obama, Cole said that "if we can give assurance to most Americans that their taxes are going to be fine, I think that's helpful to them in planning their lives going forward."

Fellow Republican Rep. Raul Labrador of Idaho disagreed with Cole, but also said letting Democrats pass a tax increase would saddle them with resulting economic stagnation.

"I think right now my advice to the leadership is that they should let the Democrats pass a tax increase because we will see that the economy will stall because of that tax increase, and then they will own it completely," Labrador said, despite his personal opposition to such a measure.

He and other Republicans complained that Obama and Democrats had yet to propose any serious proposals to also cut spending and reform entitlement programs such as Medicare and Medicaid as part of a broad deficit reduction deal.

"I think we're making a mistake that we're running around trying to think of ways to deal with the president when the president doesn't want to deal in good faith," Labrador said.