Republicans already think the administration has the flexibility to make the cuts less painful, as long as they clear these changes with Congress first. That deference to Congress could allow the proposal to survive both the Senate and a House-Senate conference later in the month.
The House and Senate have just two and a half weeks to avoid a government shutdown by reaching agreement on the House bill and whatever the Senate passes.
While the Senate wrestles with spending, President Obama will continue what many are calling his new charm offensive toward Republicans, in the hopes of finding some way around the sequester. Obama will meet with Senate Republicans for lunch Thursday, which comes after his dinner meeting this week with GOP senators.
Obama has also asked to meet with House Republicans, something that could take place next week. And, he is expected to meet with Democrats in the House and Senate on the sequester.
In the House, Democrats have been arguing for months that the GOP needs to take up jobs legislation. Next week, the House will do just that, but with bills Democrats may oppose.
One of these is aimed at blocking Obama administration guidance that says states can waive the requirement that says welfare recipients must look for work as a condition of getting welfare benefits. Democrats in committee were already hotly opposed to this bill.
The second bill is a challenge to Obama's pledge from last year to streamline federal jobs programs. This GOP bill would streamline and consolidate 35 federal jobs programs, and create one-stop shop for all federal employment programs.
Below is a more detailed look at the week ahead:
The Senate meets at 2 p.m., and hopes to start work on the House-passed continuing resolution for the rest of fiscal year 2013, H.R. 933. Senate Democrats will put forward their own proposal as a substitute to the House-passed bill.
At 5:30 p.m., the Senate will vote on the nominations of Richard Taranto and Andrew Gordon to be U.S. district judges, in the Federal Circuit and the District of Nevada, respectively.
The House meets at 10 a.m. for a pro forma session but otherwise has no votes planned.
The House meets at noon for speeches, then later in the afternoon for legislative work on two bills. They are:
H.R. 749, the Eliminate Privacy Notice Confusion Act. This bill, which the House approved late in the last Congress, would eliminate the current requirement that banks mail out annual notices on their privacy policies, even when these policies don't change. Instead, the bill would allow banks to mail out these notices only when they change their privacy policies.
H.R. 1035, which would require a study of voluntary, community-based flood insurance options, and how these options might be incorporated into the national flood insurance program.
The Senate is in Tuesday and the rest of the week to work on the 2013 spending bill.
The House meets at 10 a.m. for speeches and noon to work on H.R. 890, the Preserving Work Requirements for Welfare Programs Act. This bill would prohibit the administration from waiving the welfare work requirements.
The House will start legislative work at noon Thursday, and take up H.R. 803, the Supporting Knowledge and Investing in Lifelong Skills (SKILLS) Act, which would streamline several federal employment programs.
Work on this bill will continue into Friday, and the last votes of the week are expected by the early afternoon.