A make-or-break week awaits Republican leaders in Congress

This week offers a make-or-break moment for Republican leaders on Capitol Hill.

After stumbling several times since taking control of Congress earlier this year, House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Mitch McConnell (R-Ky.) have an opportunity to demonstrate on two important fronts that Republicans can effectively govern.

But it remains unclear if they will be able to deliver.

Boehner acknowledged Tuesday the momentous days ahead, as Republicans will try to pass their annual budget for fiscal 2016 and approve a sweeping bipartisan accord to overhaul the way doctors are paid under Medicare.

"Well, this is a big week for the House's focus on the people's priorities," Boehner said.

Unable to unite feuding Republicans around a single budget blueprint, GOP leaders in the House are resorting to a rarely used procedure -- dubbed "Queen of the Hill" -- that allows lawmakers to vote on whichever plan they prefer. The one with the most votes advances.

It was seen as the only way to resolve a standoff between the party's defense hawks and deficit sharks that has threatened to derail the entire process.

Defense backers want to boost Pentagon spending and counter the austerity cuts demanded by deficit watchers in a 2011 deal. GOP deficit watchers, meanwhile, are trying to hold the line against new government spending.