Some debate on the measure could begin "this week," Durbin, D-Ill., the Senate majority whip, told CNN's "State of the Union" Sunday, but the bill would not actually reach the floor until after the Senate's scheduled recess Sept. 26-30, he said.
"I think that's more realistic, it would be next month," he said.
The chamber returns for legislative business Oct. 3.
Obama -- who went before Congress Sept. 8 to push for the $447 billion package of tax cuts and new government spending and followed the address with several speeches touting the proposal -- plans at 10:30 a.m. EDT Monday to outline how he would pay for the bill, known as the American Jobs Act, and reduce the government's deficit.
The bulk of the plan -- some $400 billion over 10 years -- would be paid for by tax changes that would limit itemized deductions, such as those for charitable contributions and other expenditures, that may be taken by individuals making more than $200,000 a year and families making over $250,000 a year.
In Obama's proposal, the rest would come from provisions affecting oil and gas companies, hedge funds and the owners of corporate jets.
The proposal to pay for the jobs bill is part of a larger deficit-reduction plan Obama will propose Monday to cut government spending by more than $3 trillion over 10 years, administration officials said Sunday night.
The larger plan includes $1.5 trillion in new taxes, mostly on the wealthy, through a combination of closing loopholes and limiting the amount high earners can deduct.
Roughly $800 billion would come from letting tax cuts passed during the George W. Bush presidency expire, aides told The New York Times.
The other $700 billion would come from closing loopholes and limiting deductions among individuals making more than $200,000 a year and families making more than $250,000, they said.
Obama's plan also includes $580 billion in adjustments to health and so-called entitlement programs, including $248 billion to Medicare and $72 billion to Medicaid, administration officials told the Times.
The Medicare cuts would not come from an increase in the Medicare eligibility age, they said.
The plan counts savings of $1.1 trillion from the ending of the U.S. combat mission in Iraq and the withdrawal of U.S. troops from Afghanistan, the officials said.
When he unveils his proposal at the White House Rose Garden, Obama will promise to veto any legislation that seeks to cut the deficit through spending cuts alone and that includes no revenue increases from tax increases on the wealthy, the Times said.
His veto threat will put him at odds with House Speaker John Boehner, R-Ohio, who said last week he would not support legislation that included higher taxes.
Boehner had no immediate comment.