This week, Congress is scheduled to tackle a series of pivotal bills that would reshape how the federal government helps unemployed Americans and what kind of aids it provides to the sprawling agriculture industry. Lawmakers will try to do this while making good on a pledge to keep federal agencies open without the partisan brinksmanship of the recent past.

Much of the action, however, will serve as tests of the power for the two leading figures on Capitol Hill, Senate Majority Leader Harry M. Reid (D-Nev.) and House Speaker John A. Boehner (R-Ohio).

For Reid, the key test comes on the handling of the debate over legislation to extend emergency unemployment benefits for the longtime jobless. Rather than just a policy debate, the federal unemployment program has turned into a proxy fight over how Reid runs the Senate amid Republican accusations that he has turned into a legislative bully who will not let them offer amendments.

“We have one person here who runs the place and says, ‘I will decide whether your amendment is not reasonable,’ ” Sen. Daniel Coats (R-Ind.) said during a heated debate last week. After initially retiring in 1999, Coats sounded like a senator who almost regretted running again in 2010.

“This is 100 percent different from the time I was here the first time. We were able to offer any amendment to any bill at any time,” he said.

That came after Reid’s proposal to extend the unemployment benefits program to mid-November but shut down the GOP’s ability to offer any amendments because he accused them of offering “gotcha” proposals designed to score political points.

“The time is now to fish or cut bait,” Reid said, responding to Coats and other critics. “I know what the Senate used to be because I was a used-to-be senator, and it doesn’t work the way it used to, not because of anything we do wrong but because of the obstruction of President Obama’s agenda.”

Reid’s power play essentially guaranteed failure for a planned Monday vote on his $18 billion legislation, as Coats and several of the six Republicans who initially voted to advance the underlying proposal backed off their support. With 55 members of the Democratic caucus signaling support, Reid needs at least five GOP votes to choke off a filibuster.

Late Monday afternoon, after a weekend of continued talks, Reid and Minority Leader Mitch McConnell (R-Ky.) delayed the vote until at least midday Tuesday, giving negotiators more time to discuss their proposals. The latest GOP offer was an extension of just three months, paired with a legislative fix to an unpopular cut to military pensions that was needed for financing a two-year budget deal agreed to last month.

Backing away from Thursday’s tough talk, Reid rejected that as too short of a deal but politely noted “that doesn’t mean we can’t work something out.”

Boehner’s move comes on the emerging farm bill, which has been stuck for more than two years during ideological and regional disputes over crop supports and cuts to nutrition programs such as food stamps. The speaker, whose hold on legislative power has wobbled for three years, has staked his reputation on knocking out what he calls a “Soviet-style” program of dairy price supports.

“I have fought off the supply management ideas for 23 years that I’ve been in Congress, and my position hasn’t changed. And Mr. Peterson and others are well aware of it,” Boehner told reporters Thursday, referring to Rep. Collin C. Peterson (Minn.), the top Democrat on the Agriculture Committee.

At issue is to what extent the government should step in to manage milk supplies and support dairy farmers during a downturn. Farmers generally back more government help, but dairy processors — who use milk to make cheese, yogurt and ice cream — oppose the change. Boehner supports the processors and has threatened to block the bill from consideration in the House if it includes the program.

But Democrats working on the bill insist that the program must be included to ensure the bill’s passage. “He’s just adamant that this isn’t going to be in there, and there’s no way to compromise and there’s no discussion. ‘It’s my way or the highway.’ That’s his position. But that’s how we got in a lot of trouble around this place with people taking those kinds of positions,” Peterson said, predicting that the bill will sail to passage with the dairy provision in place.

“Everybody wants this over with,” he said. “People are coming up to me to say, ‘I wasn’t sure I’d vote for this, but we need to get this over with.’ If we can just get this finalized and get it on the floor, it’s going to pass.”

House and Senate negotiators have reached accord on crop insurance programs and about $9 billion in cuts to the federal food stamp program, but they are deadlocked over government support for the dairy industry, said several aides familiar with the talks.

Those two battles come as members of the House and Senate appropriations committees are putting finishing touches on a detailed $1 trillion outline for federal agency budgets for fiscal year 2014. That comes a month after a deal hatched by Rep. Paul Ryan (R-Wis.) and Sen. Patty Murray (D-Wash.) that set a framework for the next two years.

With a new top-line figure for overall agency spending, the appropriators can more easily come to terms with how to divvy up the cash. Still, the effort has been grueling in recent weeks.

Text of the legislation — known as an “omnibus” for insiders, because it compiles what are supposed to be 12 spending bills into one massive measure — was released late Monday night. Under House procedures, that would allow for a Wednesday vote there and Senate approval later in the week.

Ed O’Keefe contributed to this report.