President Obama, his second-term agenda bogged down amid political controversies and partisan gridlock, will attempt Tuesday to keep public pressure on the Senate to move forward with a sweeping proposal to overhaul the nation's immigration system.

Obama is scheduled to appear at the White House with a broad coalition of immigration supporters to tout the legislation that has reached the Senate floor this week. With the full chamber expected to engage in weeks of debate, the president is trying to exert his influence while not upsetting the delicate balance of a bipartisan group of eight senators that negotiated the deal.

Though Obama has made immigration reform one of his top second-term priorities, his administration has played mostly a supportive role as the senate group took the lead in drafting the legislation. White House aides have said the president recognizes that being too far in front on immigration could risk scaring off Republicans fearful of being tied too closely with the administration.

But opponents of the bill -- which features a 13-year path to citizenship for immigrants who are in the country illegally -- are gearing up to offer amendments aimed at delaying or denying the legalization process. And Obama, who has been stymied on his efforts at new gun-control laws and a grand bargain to reduce the deficit, has stepped up his involvement in the immigration issue again this week.

"The bill before the Senate isn’t perfect. It’s a compromise. Nobody will get everything they want – not Democrats, not Republicans, not me," he said in his weekly radio address. "But it is a bill that’s largely consistent with the principles I’ve repeatedly laid out for commonsense immigration reform."

Appearing in the East Room on Tuesday, Obama will be joined by a coalition of immigration reform supporters meant to illustrate the broad support. Among them will be U.S. Chamber of Commerce President Thomas Donohue, AFL-CIO President Richard Trumka, former Bush administration Commerce Secretary Carlos Gutierrez, business executive Steve Case, and San Antonio Mayor Julian Castro (D).