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Rep. Michael T. McCaul, Texas Republican and chairman of the House Homeland Security Committee, said Republicans would be hashing out “two key hot spots” in Wednesday’s meeting: the pathway to citizenship and health care.

“We need to be the party of solutions and not always obstructing. And so I think there’s an effort here that we have a broken immigration system. We need to fix this immigration system,” Mr. McCaul said Sunday on CBS’ “Face the Nation,” predicting that the full House could take up immigration as early as this month and lawmakers from both chambers could be working to resolve differences in the House and Senate versions late this year or early the next.

The House Judiciary Committee has adopted a piecemeal approach, approving a series of bills, none with a path to citizenship that Mr. Obama and Democrats are seeking. Democrats hope the single-issue bills get them to a conference with the Senate, where the prospects for a far-reaching overhaul improve.

“I think what you’re finding is that there will be a compromise, a smart compromise,” said Rep. Xavier Becerra, California Democrat, said Sunday, also on CBS. “You have to be smart. You have to be tough. But you have to be fair. And if you can do that, you’ll have a full fix.”

A more pressing concern for some lawmakers was the fate of the five-year, half-trillion-dollar farm bill.

In a surprise last month, the House rejected the bill as 62 Republicans voted no after Mr. Boehner had urged support for the measure.

House conservatives wanted cuts deeper than $2 billion annually, or about 3 percent, in the almost $80 billion-a-year food stamp program while Democrats were furious with a last-minute amendment that would have added additional work requirements to food stamps, now called the Supplemental Nutrition Assistance Program, or SNAP.

Mr. Reid has made it clear that an extension of the current farm law, passed in 2008, is unlikely as he presses the House to pass the Senate version of the bill. That leaves Mr. Boehner to figure out the next step before the current policy expires Sept. 30.

Congress also must figure out what to do about interest rates on college student loans, which on Monday doubled from 3.4 percent because of partisan wrangling in the Senate.

Lawmakers promised to restore lower rates when they return this week, both retroactively and before students start signing loan documents later this summer. For now, the rate stands at 6.8 percent, which is higher than most loans available from private lenders.

Congress faces political and economic fights over the budget, with the fiscal year ending Sept. 30 and Congress plodding through spending bills with no sign they will be done on time. The House is set to vote this week on the spending bill for the Energy Department.

In addition to legislation to keep the government running, Congress probably will have to vote on whether to raise the nation’s borrowing authority, a politically fraught vote that roiled the markets in August 2009.

Three Senate committees will consider Mr. Obama’s nominees for major national security positions this month, confirmation hearings certain to set off a political dust-up over the president’s policies, though the criticism is unlikely to scuttle the selections.

Questions about the administration’s policy toward Syria and plans to arm the rebels in their civil war with President Bashar Assad’s forces will dominate the Senate Armed Services Committee hearing on the re-nomination of Army Gen. Martin E. Dempsey for chairman of the Joint Chiefs of Staff.

The hearing is scheduled for July 18.

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