The Senate is expected to vote on a temporary extension of the debt limit sometime later this week. The House of Representatives already passed a bill to keep the government funded until mid-May while Congress and the White House negotiate a budget.

The big challenge will be over how to slow the growth of government spending without stalling economic recovery.

Republicans want big spending cuts in order to eliminate the deficit and balance the budget in 10 years. Democrats, in contrast, want to reduce spending in order to stabilize the level of government debt and its share of the broader economy. That’s the setup for a possible big bruising budget battle ahead.

Related: Washington's Dirty Little Secret: The Deficit Doesn't Need to be Cut: Josh Brown

Alan Blinder, former Fed Vice Chairman and author of the new book, After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead

, says progress on the deficit is possible, but a balanced budget in the next 10 years is not.

Reducing the deficit by just 2.5% of GDP—not eliminating it—translates into a $5 trillion reduction in the deficit which will be politically difficult and require compromise, Blinder writes. “Republicans will have to concede that while it is arithmetically possible to do the entire job on the spending side, it is politically impossible. Democrats will have to concede that the majority of deficit reduction must come on the spending side, including entitlements like Medicare.”

Related: America Should Declare Bankruptcy: Doug Casey

Medicare spending is the primary problem but not for another 10 years or so and "Social Security is a small problem that can easily be fixed," Blinder tells The Daily Ticker.

He says the U.S. has “no chance to get the deficit under control” until it “significantly reduces health care spending,” which will eventually “swallow up everything.”

The “cost cut benders” included in the health care reform law could potentially reduce health care costs, says Blinder, but knowing which ones succeed in doing that and which ones don't will take time and patience.

In the meantime, there are risks that budget battle ahead could cause the government to shut down or crash into the debt ceiling before the debt ceiling expires May 19, says Blinder.

Here are some important budget deadlines to watch:

• March 1: $1.2 trillion worth of in automatic spending cuts in domestic programs and defense start to take effect.

• March 27: The stopgap law to finance government operations expires.

• April 15: Congressional members won't get paid if they don’t adopt a budget blueprint by this time.