Twenty-nine lawmakers are supposed to come up with a long-term budget deal by mid-December. They meet again Wednesday around a conference table, led by two people who couldn't be more different: Democratic Sen. Patty Murray of Washington state and Republican Rep. Paul Ryan of Wisconsin.

At 6-foot-1, Ryan looms over Murray by more than a foot. He's known as a budget geek, but managed to get a photo spread in Time magazine last year doing bicep curls in a T-shirt. It was titled "Paul Ryan: All Pumped Up for His Closeup." When he was named the Republican nominee for vice president last year, it was clear he was someone who savored working large crowds, who seemed to bask in the glow of a spotlight.

And across from him now at the budget negotiating table is a former preschool teacher who's never been one to hog the microphone.

Years ago, a Washington state lawmaker called Murray "just a mom in tennis shoes," and she turned that diss into a campaign theme when she first ran for the Senate in 1992. As a fresh senator-elect back then, she promised reporters she'd wear her tennis shoes "at least once" on the Senate floor and declared she wanted to show people someone could be a mom and an effective U.S. senator at the same time.

After two decades in the Senate, Murray has built a reputation for being unassuming, practical and extremely hardworking — and she told NPR earlier this year that being a woman can be an advantage in Congress, especially when it comes to something as contentious as the budget.

"Well, you know, I don't want to put the men senators down. There are some really great men senators here, but I do see women working collaboratively and listening more to people to try to find their core common ground to get something done," says Murray.

But there isn't much hope that even a collaborative nature can bridge the ocean that divides Democrats and Republicans on taxing and spending — because what's on the table are some of the most fiercely defended elements in both parties' ideologies.

Republicans want to see real cuts to entitlement programs, like Social Security and Medicare. Democrats want to increase revenue by raising taxes. Ryan already rejected that idea at the first budget conference committee meeting.

"I want to say this from the get-go: If we look at this conference as an argument about taxes, we're not going to get anywhere," Ryan said.

Comments like that make budget experts like Stan Collender think not much is going to come out of this budget conference committee.

"The first thing everybody has to understand is that the so-called grand bargain – the big deal – is a pure fantasy," says Collender.

Perhaps lawmakers will agree to undo some of the across-the-board spending cuts, known as the sequester, Collender says. Both sides hate those cuts, which isn't surprising, he says, because the sequester was supposed to be the worst possible alternative.

"It turns out it's the worst possible alternative except when compared to everything else," says Collender. "That is, it's actually the best alternative if the only other options are to cut entitlements — that is Medicare and Social Security and Medicaid — or to increase revenues, that is, taxes."

Even if a big deal were in the works, it wouldn't happen now, not in this committee, says Ross Baker, a political science professor at Rutgers University, who calls these budget conference committee meetings mere "legislative foreplay."

Both Murray and Ryan are highly respected within their caucuses — both are considered tremendously smart and effective lawmakers. But in the end, Baker says, any agreement the two committee leaders come up with could still be rejected by either of their chambers.

"I think as much as they enjoy the respect of their colleagues, none of this is personal. It really does come down to the very, very significant differences of what it means to be a Democrat and what is means to be a Republican," says Baker.

Ultimately, it will be up to the president and the two top leaders in both chambers to make any real deal, if there's even one to be made.

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