If the debate over whether to try to defund Obamacare as part of a resolution to fund the government has been a stressful font of disunity for Senate Republicans, it's been a rallying cry for the Senate Conservatives Fund, a conservative outside group.

After Senate Minority Leader Mitch McConnell and Sen. John Cornyn, R-Texas, announced support Monday for addressing the health care law separately from government funding, the group shot off a fiery email to supporters Tuesday calling it "the ultimate betrayal."

"Mitch McConnell and John Cornyn have surrendered to Barack Obama, Harry Reid and the Democrats," the message read. "More importantly, they have surrendered to Obamacare — the biggest job killer in America."

McConnell and Cornyn's decision to try to advance debate on a bill to keep the government running put them at odds with Sen. Ted Cruz, R-Texas, who has staunchly opposed any such measure -- much to the chagrin of many Republicans, who have called his stance unrealistic.

Cruz has long been a darling of the Senate Conservatives Fund, formerly run by then-Sen. Jim DeMint, who now heads up Heritage Foundation, another conservative outside group.

Earlier this year, Cruz starred in an ad paid for by the Senate Conservatives Fund. Meanwhile, the group has spent thousands of dollars against Republican senators who it deems have not acted in line with conservative principles. This puts Cruz in a potentially awkward position: he is also a vice chairman of the National Republican Senatorial Committee, which aims to get Republican senators re-elected.

Brian Walsh, a Republican strategist formerly with the NRSC, said the Senate Conservatives Fund's interest is less about affecting policy than "about expanding their own power and influence and raising money for their own organization.”

"They're acting like bullies now," Walsh said. "They’re raising money by misleading conservatives, and they’re taking that money and threatening members of Congress."