President Obama's move toward halting deportations of as many as 5 million immigrants in the U.S. illegally is giving potential 2016 Republican presidential aspirants a big target to rail against.

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Sen. Marco RubioMarco RubioBush ethics lawyer: Congress must tell Trump not to fire Mueller The private alternative to the National Flood Insurance Program  Cruz offers bill to weaken labor board's power MORE (R-Fla.) is calling the plan a "terrible idea," warning it would badly damage any possibility of compromise on immigration legislation.

"As someone who supports immigration reform, that wants to see us achieve something, I believe it will set us back. I believe it will make it harder for us to achieve the sorts of reforms our country needs," Rubio told reporters on Thursday. "It will be deeply divisive. I've been saying that for months, and I'm glad others are beginning to say the same thing because it's true. If he takes executive action, I believe it will make it harder, even impossible in the short term, to achieve what we're trying to achieve in immigration reform."

Rubio, a leading negotiator on the bipartisan immigration reform bill that passed the Senate but stalled in the House, has been hammering Obama on his approach to immigration and border security since last summer's border crisis, when thousands of young Central Americans illegally entered the U.S. His attacks against Obama could help reassure the conservative base that he's not that out of line with their border hawk views.

Others are chiming in as well.

Sen. Ted CruzTed CruzGOP wrestles with soaring deductibles in healthcare bill Cruz: Tax reform chances ‘drop significantly’ if healthcare fails Ex-CBO directors defend against GOP attacks on ObamaCare analysis MORE (R-Texas), a hard-line border hawk, has been working with other conservative senators to include prohibitions on what he calls "executive amnesty" in next month's budget negotiations.

"President Obama will be exercising powers properly belonging to Congress if he makes good on his threat. This will create a constitutional crisis that demands action by Congress to restore the separation of powers," Cruz said in a statement released last week.

Former Sen. Rick Santorum (R-Pa.), another likely presidential candidate, is launching a petition drive to push the White House to back down, with the website NoObamaAmnesty.com.

"President Obama's intention to use an Executive Order to grant amnesty goes completely against the way the American people voted in this month's historic election," Santorum said in a Friday morning statement. "This unilateral action sends a message that the President believes his opinion should supersede the will of the American people and democratic process. While we all agree our immigration system needs to change, granting amnesty with the stroke of the President's pen is not the answer."