White House Chief of Staff Denis McDonough headed to Capitol Hill to rally support for the bill Thursday night.
"The president is making calls, as is the White House staff" to both Democrats and "a few Republicans," Earnest said on MSNBC's "Now with Alex Wagner."
President Obama came out in support of the bill Thursday afternoon in advance of a scheduled vote later in the day.
Earnest said that the spending measure is not "perfect," but is a "pretty good deal."
"It's a compromise proposal," he said.
When asked if the bill will pass Thursday, Earnest said, "We'll see." But he said he did not think the government would shut down, and that Congress would instead put in place a three-month temporary funding measure.
Officials have said they still believe the measure will pass before a midnight deadline, despite the fact it barely survived a procedural vote earlier in the day.
House Minority Leader Nancy Pelosi (D-Calif.) said Thursday she opposes the bill because it would undo parts of the Dodd-Frank financial regulatory overhaul. Earnest said the White House doesn't support the provision that would undo parts of Dodd-Frank, but that the spending package would shore up some aspects of Wall Street regulation.
"We don't have the same sort of assessment that this is a doomsday provision," Earnest said on Bloomberg's 'With All Due Respect.' "There are a lot of good things related to Wall Street reform in the bill."
Earnest said the White House is “casting a wide net and encouraging as many Democrats as possible to take a close look at this legislation because there’s a lot in there to like."
Meanwhile, the White House Office of Management and Budget held a conference call today with federal agencies about planning for a possible government shutdown.
"Congress is taking a series of actions today on legislation that would prevent a lapse in appropriations and allow for continued Government operations. We continue to believe that time remains for Congress to pass full-year appropriations for FY 2015, and prevent a government shutdown," an official with the White House Office of Management and Budget said. "However, out of an abundance of caution, we are working with agencies and taking steps to prepare for all contingencies, including a potential lapse in funding.”
The Office of Management and Budget also held a call with agencies Dec. 4 about a possible shutdown.
That move doesn't give any indication of whether or not they believe a shutdown's likely -- it's a required action. The White House rules for the preparation of the budget state that the office will "monitor the status of Congressional action on appropriations bills" and will "notify agencies if shutdown plans are to be implemented."
A week before the deadline for the bill to be passed -- whether or not it looks like a shutdown will happen -- the office is required convene a call or teleconference with federal agencies, and hold follow-ups if necessary.
Ed O'Keefe contributed to this report