President Barack Obama is set to unveil “a more ambitious deficit plan” Monday, but it’s unclear whether the president’s framework — or any other exhortations for the Joint Committee on Deficit Reduction to “go big” — will push it to go further than the original $1.5 trillion target.

Obama announced in an address to a joint session of Congress this month that his budget outline would include entitlement and revenue reform — two of the most politically divisive issues in the budget debate. Obama’s outline is expected to call for about $2 trillion in savings.

Although members of the super committee expressed openness to tackling both taxes and entitlements during the group’s first two public hearings, almost all of them acknowledge that the road to any agreement will be difficult. And sources close to the committee suggest that any outside pressures, even from the president, will make that road much tougher.

In that respect, the 12-member bipartisan, bicameral panel has started to create a bubble around its work. The panel’s lawmakers have kept extremely tight-lipped after leaving private meetings, and there has been little internal discussion of outside calls — from the White House or other policymakers — for them to include or exclude certain items. The panel’s co-chairmen, Sen. Patty Murray (D-Wash.) and Rep. Jeb Hensarling (R-Texas), have said little about the panel’s goals beyond statements last week that they were ready to “seize the moment.”

Leadership sources said it is unlikely the super committee will be swayed by positions taken by anyone outside the room unless that direction is coming from some agreed position among Obama, Speaker John Boehner and Senate Majority Leader Harry Reid (D-Nev.) — a scenario not inconsistent with Congress’ last two big agreements on the nation’s finances. Those deals include a compromise that averted a government shutdown and an agreement on raising the debt ceiling.

“It’s more of a box-checker than a game-changer,” one Democratic leadership aide said about Obama’s speech Monday.

Also consistent with recent precedent, aides to Hill leaders said that, as of Friday, the White House had not told them the details of the plan Obama is set to release. However, they said they expect the speech to be similar in tone to a broader budget address Obama delivered last spring at George Washington University rather than a concrete outline of what he’d like to see done.

From the vantage of the super committee, the more generic Obama is, the better. For as much as the panel’s members consider the president’s offering, they will have an easier time getting Republicans on board with what might be bipartisan ideas if those concepts are not considered to be owned by Obama. The fewer details the president lays out publicly, the wider open he leaves the door for the group’s Republicans — who are already in a tight spot but so far are demonstrating a willingness to find agreement — to negotiate.

During his address in the House chamber earlier this month, Obama hinted at what his plan might entail.

“I’ll be releasing a more ambitious deficit plan — a plan that will not only cover the cost of this jobs bill, but stabilize our debt in the long run,” Obama said Sept. 8.

“This approach is basically the one I’ve been advocating for months,” Obama added. “In addition to the trillion dollars of spending cuts I’ve already signed into law, it’s a balanced plan that would reduce the deficit by making additional spending cuts, by making modest adjustments to health care programs like Medicare and Medicaid and by reforming our tax code in a way that asks the wealthiest Americans and biggest corporations to pay their fair share.”

At the time Obama delivered his speech, many Republicans in the House and Senate were slow to outright reject his jobs proposals, instead sending signals to the White House that they would be willing to move pieces of his proposals — such as payroll tax cuts for employees and employers. In turn, the White House signaled an openness to signing into law any chunks they send him.

If the president were to be “presented with parts of his plan, his instinct would be not to reject things he favored, but to come back and keep fighting and fighting to get the entire program,” top economic adviser Gene Sperling told a roundtable of reporters last week.

The super committee is slated to hold its next public hearing Thursday, but lawmakers have begun to meet behind closed doors more frequently, with full and intraparty sessions held last week.