WASHINGTON — President Barack Obama is using his presidential pulpit to press the Republican-controlled House to embrace a path to citizenship for all 11 million people living illegally in the U.S., while a top Republican says only those brought to America as children should be given the highest priority.

With prospects shaky for passing an immigration overhaul in the House, the White House insisted Monday that to garner Obama's signature, any bill must satisfy the president's principles — the path to citizenship chief among them. But Obama is leaving the particulars of how Congress gets there up to lawmakers, wary of strong-arming the process and handling Republicans an excuse to vote no.

"I cannot even begin to count the number of possibilities that could emerge through the House process. So I'm not going to," said White House spokesman Jay Carney. "What I'm saying is that the end result has to meet the president's principles if he's going to sign it into law."