Recently elected Democrats have clamored for changes in Senate rules as Obama has faced Republican resistance to his nominations.
Two Cabinet-rank choices—Tom Perez as labor secretary and Gina McCarthy to head the Environmental Protection Agency—could be approved by the Senate this month after a loud debate over administration policies.
The GOP also has challenged Obama's three judicial nominees to the U.S. Court of Appeals for the District of Columbia Circuit as they've tried to eliminate the vacancies. The Senate scheduled a vote late Monday on a less contentious nomination—Gregory Phillips to serve as U.S. circuit judge for the 10th Circuit.
Reid had served notice in April that the Democratic majority could change the Senate rules on "any given day" and that he was willing to do so if necessary.
In the GOP-controlled House, courteous behavior, even within the majority ranks, has barely been perceptible with the ignominious failure of the farm bill. Some collaboration will be necessary if the House is to move ahead on immigration legislation this month.
Conservatives from safe, gerrymandered House districts have rebuffed appeals from some national Republicans who argue that embracing immigration overhaul will boost the party's political standing with an increasingly diverse electorate, especially in the 2016 presidential election. Those conservatives strongly oppose any legislation offering citizenship to immigrants living here illegally.
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Reflecting the will of the rank and file, House Speaker John Boehner of Ohio and other Republicans have said the comprehensive Senate immigration bill that couples the promise of citizenship for those living here unlawfully with increased border security is a nonstarter in the House.
Opening the Senate session on Monday, Reid urged the House to consider the Senate bill—a highly unlikely step.
"Now it's our duty to convince our colleagues in the House, yes, they should vote with us," he said. "Bipartisan immigration reform that includes a pathway to citizenship makes economic and political sense."
House Republicans were assessing the views of their constituents during the weeklong July 4th break and planned to discuss their next steps at a private meeting Wednesday.
Rep. Michael McCaul, R-Texas, chairman of the House Homeland Security Committee, said Republicans would be hashing out "two key hot spots" in the 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 ... need to fix this immigration system," McCaul said Sunday on CBS' "Face the Nation." He predicted that the full House could take up immigration as early as this month, and that representatives from both chambers could be working to resolve differences in their versions late this year or early next.
The House Judiciary Committee has adopted a piecemeal approach, approving a series of bills, none with a path to citizenship that 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," Rep. Xavier Becerra, D-Calif., 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, $500 billion farm bill.
In a surprise last month, the House rejected the bill as 62 Republicans voted no after 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; Democrats were furious with a last-minute amendment that would have added more work requirements to food stamps, now called the Supplemental Nutrition Assistance Program.
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 Boehner to figure out the next step before the current policy expires Sept. 30.
Some conservatives are pushing the speaker to split the bill in half and bring up separate bills—one dealing with farm programs and one that would set policy for food stamps.