The measure also would include enough money to operate the Defense Department through the Sept. 30 end of the fiscal year, the officials added.
They said House Speaker John Boehner, R-Ohio, told the rank and file in a closed-door meeting he would seek passage of the bill if it became clear it was necessary to avoid shutting the government down.
He presented the plan at the end of a day marked by increasing acrimony in negotiations involving the Obama administration, Senate Democrats and Republicans.
With little progress evident toward a bill to close out the budget year, President Barack Obama invited key lawmakers to the White House in search of a deal.
"Time is of the essence," said White House press secretary Jay Carney, announcing plans for the Tuesday meeting. "We need to get this work done."
Congress has already passed a pair of stopgap bills to keep the government in operation for a total of five weeks, with a total of $10 billion in spending cuts attached at Republican insistence.
A one-week measure that contains an additional $12 billion would presumably be reassuring to tea party-backed lawmakers who are among the most vocal in seeking to reduce the size and scope of the government.
It would also be difficult for most Democrats to support. But by including the money the Pentagon needs for the next six months, Republicans hoped to increase the pressure on them.
For Republicans, work on the spending bill was only part of an effort to emphasize a determination to cut federal spending. They also arranged to unveil a sweeping 10-year plan on Tuesday to slash deficits by a staggering $4 trillion or $5 trillion over a decade.
Even before the details of the plan became known, Democrats began attacking it.
But for the moment, the main focus was on the threat of a shutdown, the product of intense disagreement sparked by Republican demands for spending cuts.
Boehner relayed word he would attend the White House meeting, but he also emphasized in a statement that the $33 billion total often cited "is not enough and many of the cuts that the White House and Senate Democrats are talking about are full of smoke and mirrors."
Boehner has said repeatedly he does not want a shutdown. Yet a new public opinion poll underscored the political dilemma confronting the leader of a conservative majority swept into power with the support of tea party supporters.
In a survey by the Pew Research Center for the People & the Press, 68 percent of tea party adherents said lawmakers should stick to their principles in the budget negotiations, even if it means the government shuts down.
Yet in the population as a whole, only 36 percent supported that view, according to the survey, and only 38 percent of independents, who comprise a key swing vote in any election.
In remarks on the Senate floor, Majority Leader Harry Reid emphasized a similar point. Tea party Republicans, the Nevada Democrat said, "stomp their feet and call 'compromise' a dirty word and insist on a budget that will hurt America rather than help it."
He said a deeper-cutting, House-passed bill "slashes programs for the sake of slashing programs. It chops zeroes off the budget for nothing more than bragging rights."
Joining Boehner in a Republican rebuttal was Rep. Hal Rogers, R-Ky., chairman of the House Appropriations Committee. He accused Reid of "dictating the use of gimmicks and phony accounting to sneak more spending through the Congress and by the American people."
The House passed the legislation more than a month ago calling for $61 billion in cuts from current levels.
In addition, that measure includes dozens of proposals not directly related to spending, including curbs on the Environmental Protection Agency and other federal regulatory agencies and a denial of funding to Planned Parenthood.
Unlike the House, the Senate has yet to pass a spending bill to close out the current budget year, now more than half over, and Democrats are divided on how deeply to cut. In several weeks of maneuvering, Congress has agreed on a pair of stopgap bills that cut $10 billion, and Obama has signed them.
Rep. Paul Ryan, R-Wis., chairman of the House Budget Committee, has said the blueprint he intends to unveil would cut in excess of $4 trillion from the budget, far more than the $2.2 trillion that Obama claimed in his own blueprint and on a par with recommendations of a bipartisan deficit commission last winter.
Other officials said that under Ryan's proposal, the annual deficit would fall below $1 trillion at the end of the coming fiscal year but would not be erased by the end of the decade.
The deficit is currently projected at $1.6 trillion for the current fiscal year, and the administration estimates that under Obama's budget, it would drop to $1.1 trillion next year and $774 billion in 2021.
Republican officials said about $1 trillion in savings under their emerging plan would come from changes to Medicaid, the federal-state program that provides health care for the poor.
Spending on hundreds of domestic programs - the accounts at the heart of the talks to avoid a government shutdown - would be returned to levels in effect in 2008, at a savings of hundreds of billions of dollars.
One of the most significant changes would occur in Medicare, which provides health care for seniors, but would not affect current beneficiaries or workers age 55 and older.
Republicans intend to move quickly to advance their new blueprint. They hope to have the Budget Committee approve it Wednesday and push it through the House next week.
The plan is expected to serve as a rallying point for Republicans who took power in January, but it is also likely to give Democrats a ready target to attack.
Democratic Leader Nancy Pelosi has drawn attention in recent days to public opinion surveys reporting widespread skepticism about fundamental changes in Medicare.