MIAMI - President Bush, pushing for a hard-to-find breakthrough on a broad immigration overhaul, appealed yesterday to graduating college students in this diverse city for help in persuading Congress to produce a bill.

Bush gave the commencement address at Miami Dade College, where more than half the students were raised speaking a language other than English. He gave the Class of 2007 an assignment: tell their elected representatives in Washington to get going on immigration overhaul.

"You see every day the values of hard work, and family, and faith that immigrants bring," the president said. "This experience gives you a special responsibility to make your voices heard."

Bush said the immigration system is deeply broken: Employers are not held accountable enough; borders are not secure enough; businesses need workers willing to do low-paying jobs; and the 12 million people estimated to be in the United States illegally cannot all be deported, and so must be dealt with "without amnesty and without animosity."

"We must address all elements of this problem together - or none of them will be solved at all," Bush said.

The president also chose the setting of Miami, a center of Cuban exiles opposed to the communist regime of Fidel Castro, to predict that the "day is nearing" when "the light of liberty will shine" again in Cuba.

"In Havana and other Cuban cities, there are people just like you who are attending school and dreaming of a better life. Unfortunately, those dreams are stifled by a cruel dictatorship that denies all freedom in the name of a dark and discredited ideology," the president said to loud cheers. "The reign of every tyrant comes to an end."

The takeover of Congress by Democrats was supposed to be a boon to Bush's goal of a comprehensive immigration overhaul. He wants to establish a temporary-worker program for some illegal immigrants and to create a path to citizenship - albeit a difficult one - for many.

It is his fellow Republicans, conservatives, who reject the president's approach as too lenient toward lawbreakers, that stymied his plans when they controlled Capitol Hill.

But the Democrats' ascendance in January has not necessarily made easier the search for a bill acceptable to a majority.

The Senate passed a plan last May that tracked closely with Bush's wishes. The proposal died in the House, where tough new border-security measures were the priority. A get-tough bill authorizing 700 additional miles of fencing along the U.S.-Mexico border was Congress' only accomplishment on immigration.

Since then, the White House has highlighted the effectiveness of stepped-up border enforcement while quietly seeking compromise on broader legislation.

So far, however, the only approach that has grown out of those initial talks would be tougher on illegal immigrants than the Senate bill. Its path to citizenship would require fines, trips back home, long waits, and hefty penalties. Some conservatives still call this overly permissive.

Bush said the talks in Washington were beginning to bear fruit.

"I know convictions run deep on the matter of immigration. Yet I am confident we can have a serious, civil and conclusive debate," he said in his weekly radio address.

Most national polls show people in the United States are overwhelmingly supportive of an immigration overhaul that would allow those already in the country illegally to stay, work, and earn their way to legal status.