But the terrorist attack in Paris this week complicated that strategy.
The Republican plan was to use the Homeland Security Department's funding as leverage to force Obama to abandon his executive action, which will defer deportations for up to 5 million immigrants in the county illegally.
A House vote is expected as soon as next week to renew funding for the department, which handles immigration. Though the rest of the government was funded last year through September, money for the Homeland Security Department was extended only until February to give Republicans more leverage to stop Obama's immigration plan.
Pleading with lawmakers not to go down this road, Homeland Security Secretary Jeh Johnson has been making the rounds on Capitol Hill this week.
More than ever, Johnson said, the department needs stable funding to keep the country safe.
"I do not want to see the budget of Homeland Security used as a political football," Johnson said on CNN. "For the homeland security of this nation, we need an appropriations bill and we need it soon."
But his entreaties may not be swaying Republicans, who view Obama's November executive action as overreach.
There has been no shortage of legislative proposals in the House and Senate to stop Obama's immigration action, some introduced amid the ceremonial fanfare of the first day of Congress.
Most focus on preventing Johnson's department from accessing any funds or fees to carry out the immigration initiative.
Obama would likely veto such measures, presuming they were not first blocked in the Senate by filibuster. The immigration plan is among his signature achievements, and Latino voters in particular have praised his action. Some immigrants can begin applying for deportation relief as soon as February.
A volley between the White House and Congress seemed to pose little political discomfort for Republicans, who could face blame if the Homeland Security Department funding runs out.
The new chairman of the Senate Homeland Security Committee, Sen. Ron Johnson (R-Wisc.), suggested Thursday that perhaps a veto is what it will take to bring attention to the situation.
"Sometimes you have to go through that process," said the chairman, who was among those who met personally with the Homeland Security secretary on the Hill. "We should fight hard for our beliefs, and we will."
As the shootings in Paris renewed questions of the ability of the U.S. to protect itself from terrorists, many lawmakers, including the Senate chairman, doubted Homeland Security would shut down amid the funding battle since most of the workers are exempt from furlough orders because they are considered essential national security employees.
Getting to next week's votes poses its own troubles for Speaker John A. Boehner beyond the optics of tangling over Homeland Security funds.
Boehner's leadership team is trying to devise a policy that would please a divided Republican majority that is anxious to confront Obama.
Some conservative Republicans want to do more than simply eliminate funds for Obama's new immigration plans, and instead also cut older immigration programs, including one in 2012 that deferred deportations of young immigrants brought to the country illegally as children.
Boehner said Thursday he promised Republicans would fight the president on immigration.
"The president has taken actions that are beyond the scope of his ability and Congress cannot just sit here and look the other way," Boehner said.
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