Will 11th hour bill keep the lights on temporarily?

House Majority Whip Kevin McCarthy, R-Calif.
Bill Clark | CQ Roll Call | Getty Images

A government shutdown at midnight tonight looks increasingly likely. But it's not a certain bet.

There were some signs on Sunday—including remarks from House Majority Whip Kevin McCarthy, R-Calif.—that the House may try and find a last minute solution to keep the federal lights on at least for a few more days.

The 11th hour solution could be a clean bill funding the government for a few more days to allow for a longer-term solution. Or it could come in the form of a list minute bill from the House that includes just one or two more modest demands of changes to Obamacare, including a repeal of the tax on medical devices that helps fund the health care law.

Any hope for a compromise?

Such a bill would amount to the House daring the Senate to choose a shutdown over changes to Obamacare that have broad support in Congress.

All the late efforts by Republicans, especially in the leadership team, reflect fear that the GOP will shoulder all the blame for a shutdown and have its already low public standing plunge even further.

One thing we know for sure about today: The Senate will reconvene this afternoon and kill the bill passed by the House over the weekend to fund the government in return for a one-year delay in the president's health care bill along with other provisions Democrats will never accept.

Majority Leader Harry Reid, D-Nev., and the Senate Democratic majority will then send a clean government funding bill back to the House where Speaker John Boehner, R-Ohio, will have just a few hours to figure out how to respond.

(Read more: Why markets should pray for a government shutdown)

Still a chance to avoid shutdown: Rep. Griffin

If no deal is reached, the federal government will begin closing down non-essential operations and send hundreds of thousands of workers home.

The economic impact will likely be minimal if the shutdown lasts just a few days. It could even prove beneficial if it defuses partisan passions and ends in a way that eases the path to raising the debt ceiling, which must be done by Oct. 17th to avoid default, according to the Treasury Department.

More troubling scenarios include a prolonged shutdown that bleeds into the debt ceiling deadline and sows enormous uncertainty among investors and business owners, sending stocks lower, interest rates higher and slamming economic growth.

There is also a possible negative scenario in which as shutdown is avoided at the least minute with a deal that conservative Republicans view as a total capitulation to Obama and Senate Democrats.

There will be a shutdown: Gutierrez

Should this happen—and it's entirely possible—all of the energy in the GOP would turn to forcing Obama to the table over the debt ceiling and trying to exact major concessions on the health care law and entitlement spending.

That's a very risky scenario as the White House is adamant about not allowing the GOP to turn the U.S. credit rating into a "hostage." One side or the other would likely blink in a debt ceiling showdown but if they do it would not be until the last harrowing moment.

So the goldilocks scenario, from a market perspective, is either a deal on funding the government that offers some victory to House conservatives or a brief shutdown that satisfies their desire for confrontation while making it clear another fight on the debt limit is not politically wise.

— By Ben White, POLITICO's chief economic correspondent and a CNBC contributor. White also authors the daily tip sheet POLITICO Morning Money [politico.com/morningmoney] Follow him onTwitter @morningmoneyben.