 -- Senate Majority Leader Harry Reid has privately asked the White House to delay an executive order on immigration until Congress passes a spending bill to keep the government running, ABC News has learned.

While Reid supports President Obama’s ability to act on his own on immigration, he told senators today that he is increasingly concerned some Republicans will seize on the move and try to block the funding bill, which could lead to a government shutdown.

"In recent days it has become increasingly clear that a small but vocal minority of Republicans are looking for an excuse to derail what has been a productive, bipartisan process of drafting a year-long funding bill to keep the government open,” Reid said in a statement to ABC News. “It is incumbent on responsible leaders within the Republican Party to work with Democrats and complete the business of keeping the government open in the coming weeks, regardless of when the president acts to provide relief to families.”

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Republican leaders have sharply warned the president not to bypass Congress on immigration, but they showed new divisions today over whether a rift could lead to a government shutdown.

Senate Republican leader Mitch McConnell ruled out the possibility of a government shutdown, even if the president signs an executive order to protect 5 million undocumented immigrants from deportation.

“We’ll not be shutting the government down, threatening to default on the national debt,” McConnell told reporters today.

But when pressed whether a fight over immigration could break that pledge, he said again: “We’ll not be shutting the government down or threatening to default on the national debt.”

Hours later, House Speaker John Boehner disagreed and said a government shutdown could not be ruled out. Several rank-and-file Republicans are already threatening to try and hold up the spending bill over immigration.

He said all options were on the table, declaring: “We’re going to fight the president tooth and nail if he continues down this path.”

A government shutdown was not the preferred route, Boehner said, but he said it could not be ruled out.

“Our goal here is to stop the president from violating his own oath of office and violating the Constitution,” Boehner said. “It’s not to shut down the government.”

Reid first expressed his concern about immigration during an off-camera conversation with a CNN producer, saying: “I’d like to get the finances of this country out of the way before he does it, but that’s up to him.”

ABC News' John Parkinson and Arlette Saenz contributed to this report.