On one end are Harry Reid and Nancy Pelosi. On the other are Sens. Ted Cruz, Mike Lee and the Tea Party contingent.
The stand-off between these factions has driven the partial government shutdown, which as of Friday afternoon was still not resolved. But there's plenty of middle ground between them.
So, can lawmakers find it?
A break in the two-week impasse began to appear as lawmakers, for the first time since Oct. 1, really started talking to each other, and to the White House. President Obama hosted, separately, members of all four congressional caucuses between Wednesday and Friday.
The meetings resulted in a flurry of compromise plans being floated. It's unclear what version all sides might ultimately decide on, or whether a flare-up could once again scotch the talks.
But the following is an overview of where the middle ground could lie, on each of the major sticking points.
Democrats' starting position: The White House and Democratic leaders like Reid and Pelosi have insisted that ObamaCare be left entirely intact during budget talks. Obama regards the overhaul as settled law and said he would not negotiate.
Republicans' starting position: In an effort spearheaded by Cruz, Lee and Tea Party allies, Republicans initially demanded that ObamaCare be defunded. The House passed a budget bill doing so, though the Senate rejected that version.
The middle ground: Several ideas have been floated between the two poles on ObamaCare. One was to delay the individual mandate -- the requirement on individuals to buy health insurance -- by a year.
With the insurance exchanges already underway, though, the administration is very resistant to the idea.
One possibility could simply be to delay the sign-up deadline by a few weeks or months. The Associated Press reported earlier this week that the real deadline to sign up, in order to avoid a fine, is mid-February -- though officials previously said it was March 31. Sen. Lamar Alexander, R-Tenn., in a statement Thursday, blasted the administration for "burying" the vital update.
A proposal that already has bipartisan support, though, is to repeal the medical device tax, a provision in the law expected to rake in $30 billion over the next decade -- but at a crippling cost to the medical device industry. An amendment opposing the tax won the support of 79 senators; Sen. Susan Collins, R-Maine, is calling for the repeal again as part of any deal.
This time, though, she's proposing a change in pension policies to offset the lost revenue.
Sen. Lindsey Graham, R-S.C., said Friday that at least delaying the tax is "common sense."
Lawmakers are also talking about imposing more fraud-prevention measures.
Democrats' starting position: Some Democrats wanted to use the budget process to undo the sequester, across-the-board cuts that took effect in March after lawmakers failed to reach a broader deficit-reduction deal.
Republicans' starting position: House Republicans voted last month to keep the sequester cuts in place.
The middle ground: The first step toward resolving the battle over the sequester may be to provide more flexibility.
Collins and other senators are talking about giving agencies the flexibility to pick and choose what to slash, subject to the oversight of Congress -- as opposed to keeping them locked into across-the-board cuts.
But Fox News has learned that a number of senators, following Friday's meeting at the White House, are now also talking about a plan to potentially swap out some "discretionary" spending cuts -- cuts to federal agencies and the like -- for cuts to entitlements.
Entitlements like Medicare, Medicaid and Social Security are the biggest drivers of the debt. Part of the reason the sequester was so tough on everything from the Pentagon to the Department of the Interior is because it never touched that side of the equation.
Rep. Paul Ryan, R-Wis., in a Wall Street Journal column, likewise proposed providing "relief" to federal agencies from the spending cuts by offsetting some of it with "structural reforms" to entitlements.
Democrats' starting position: Obama and other Democrats wanted Congress to approve a no-strings-attached increase in the debt ceiling -- despite having negotiated with Republicans in 2011 over spending cuts.
Republicans' starting position: Republicans started out by planning to attach a host of measures to the debt-ceiling increase -- everything from spending cuts to a delay in ObamaCare to a provision giving the green light to the controversial Keystone pipeline.
The middle ground: Initially, House Speaker John Boehner proffered a short-term increase in the debt ceiling -- one mostly free of additional riders -- as the middle ground in this debate. But Obama pushed back, since he wants to address the partial government shutdown as well.
Republican senators emerging from Friday's meeting said Obama continues to insist that he will not negotiate on the debt ceiling.
But Ryan, in his Wall Street Journal op-ed, laid out one possible course. Aside from modest changes to entitlements -- like having top earners pay higher premiums for Medicare -- he pointed to the long-running efforts by Rep. Dave Camp, R-Mich., and Sen. Max Baucus, D-Mont., to reform the tax code -- namely, by lowering rates, broadening the base and simplifying the code. This has long been the goal of the tax-reform crowd, but Congress somehow always manages to avoid the debate.
Ryan, though, pointed out that Obama has indicated an inclination to engage, by pushing for a reduction in the corporate tax rate. He urged Congress to, at last, take up tax reform alongside curbing entitlements, as part of a deal to resolve the impasse.
"This is our moment to get a down payment on the debt and boost the economy," Ryan wrote. "But we have to act now."