WASHINGTON — Senate Majority Leader Harry Reid said Tuesday that President Obama should take executive action as quickly as possible to remake the nation’s immigration system.

It was a shift from last week when Reid said Obama should wait to act until Congress had completed work on must-pass spending legislation to fund the government into next year.

“I believe that when the president decides to do his executive order, he should go big, as big as he can,” Reid told reporters on Capitol Hill, adding that he had spoken with Obama on Monday. “I said he should do something as quickly as he can.”

However, other Democrats suggested Obama should wait, amid some concern that Obama’s unilateral action on immigration could impede progress on a spending bill that Congress must pass by Dec. 11 to keep the government running.

“She doesn’t want anything to get in the way of getting an omnibus approved,” said Vincent Morris, spokesman for Senate Appropriations Committee Chairwoman Barbara Mikulski, D-Md..

“I wish he would let the process work for a few months before he did this,” said Sen. Jon Tester, D-Mont.

The White House has not said when Obama will act, but activists and Democrats expect it could come as early as this week. The president is expected to take administrative steps to protect as many as 5 million people in the country illegally from deportation, and grant them work permits.

The planned move has infuriated Republicans fresh off midterm victories in which they retook the Senate and increased their majority in the House. Republican lawmakers in the House and Senate huddled Tuesday to weigh possible responses, with party leaders aiming for a solution that avoids a government shutdown.

House Appropriations Committee Chairman Hal Rogers, R-Ky., advanced a new approach at a Republicans’ meeting Tuesday morning. Called “rescissions,” it would allow Congress to pass the full-year spending bill favored by Rogers and other leaders, and then later go back and delete funding for specific programs, trying to undo Obama’s action that way.

Another approach would be to extend full-year funding for most government programs but to try to single out the Homeland Security divisions that would be responsible for paying for Obama’s executive action, and fund them only on a short-term basis, or make their funding contingent on stopping Obama’s action.