Indiana Governor Mike Pence told NBC News on Wednesday that Congress should use "the power of the purse" to prevent the president from taking executive action on immigration.
The governor did not rule out a government shutdown, which one Republican leader had held open on Sunday as a possible means of stopping such presidential action.
Pence is one of more than half-a-dozen potential presidential candidates gathering in Florida to celebrate Republican victories in governor's races this fall.
"But I will say this, as the president has said many times, legislative action is always preferable, but we've waited now for years for the Congress to act. And the Congress has not acted," Department of Homeland Security Secretary Jeh Johnson said at a National Press Club event in the morning.
Johnson went on to list the various efforts in the Senate to pass immigration reform only to not make it through the House.
Earlier on Wednesday, CNBC confirmed that the president planned to announce an executive order in Las Vegas on Friday to address immigration.
Another source familiar with the situation told CNBC that Obama could yet give a broader outline on an immigration order on Thursday and add detail on Friday.
The president has been long expected to make an announcement that would protect up to five million unauthorized immigrants from the threat of deportation and provide work permits.
Partisan fighting erupted in the summer over how to address the increased flow of unaccompanied minors from Central America at the U.S. border with Mexico.
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Obama has asked for $3.7 billion to address the border crisis. In the summer, the Republican-controlled House of Representatives, however, passed a measure that only gave Obama a fraction of what he sought and made it easier to deport the young migrants arriving at the border, a provision opposed by Democrats and immigration advocates. In the end, Congress adjourned without a final bill.
The Democratic-led Senate last year passed a broad overhaul of immigration with support from some Republicans that boosted border security, increased visas for legal immigrants and a provided a path to citizenship for immigrants illegally in the country.
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But the Republican-controlled House balked at acting on any broad measure and House Speaker John Boehner informed Obama earlier this year that the House would not act in 2014. That led Obama to declare he would act on his own by issuing executive orders.
Wires contributed to this report.