President Obama is learning the hard way that no matter which political party is in the White House, it isn't easy to cut reimbursements to states for locking up law-breaking illegal immigrants.

Obama, to trim the $3.4 billion budget plan making its way through Congress, had proposed this week a package of $17 billion in domestic cuts. Republicans said the proposal didn't cut enough, while Democrats objected to cutting some of the programs.

Obama may find the toughest program to cut is the State Criminal Alien Assistance Program, which gives money to states to help defray the cost of incarcerating illegal immigrants who commit crimes. The $400 million program is one of the largest non-defense discretionary spending item to be cut under Obama's proposal.

Former President Bush tried in vain to kill the program several times, facing opposition from, among others, Obama and Secretary of State Hillary Clinton -- who, as senators, tried to secure additional funding for the program -- and Homeland Security Janet Napolitano, who was Arizona governor at the time.

Now Obama is facing similar opposition.

Arizona Reps. Gabrielle Giffords, Harry Mitchell and Ann Kirkpatrick sent a letter to key House lawmakers urging them maintain funding for the program. As of Friday, 17 members of Congress had signed the letter, including 12 Democrats and five Republicans from eight states.

"As Arizonans, we know the tremendous financial toll illegal immigration is taking on our state and local law enforcement agencies," Giffords said. "As long as sheriff's offices in Pima, Cochise and other Arizona counties are doing the federal government's job of securing our border, they must get compensated for it. That is the fair thing to do."

But Peter Orszag, director of the White House's Office and Management and Budget, said despite the proposed cut, the administration is still committed to spending money on the border, noting that the president's budget includes $27 billion for border and related security, an 8 percent increase over last year.

The State Criminal Alien Assistance Program is flawed, Orszag said

"The evidence suggests that the funds are often used in a variety of ways that are tangential to the direct cost associated with imprisoning unauthorized immigrants," he said. "And the reason that we proposed terminating that program is precisely that it is not well targeted to the problem at hand, in addition to the desire on our part to focus our efforts and attention on reducing unauthorized immigration in the first place."

But some aren't satisfied with that explanation.

"Illegal immigration and border security are federal responsibilities," said Ed Kowalski, director of 9/11 Families for a Secure America. "Forcing state governments to pick up the tab for the federal government's failures doesn't save U.S. taxpayers one dime.

"Further, President Obama has not offered any alternative to reimbursing the states for the high costs associated with prosecuting and incarcerating criminal aliens."

Sen. Dianne Feinstein, who repeatedly has pushed for additional funding for the program, said Obama's proposal deprives "communities of critical funding for public safety services."

"We cannot afford to let our public safety services crumble under the weight of our immigration policies, especially during this time of economic uncertainty," she said. "I am committed to restoring the funding for this essential program."