WASHINGTON — President Barack Obama is assembling an ambitious second-term agenda, pushing aggressively where he thinks he has political leverage but moving more cautiously on issues where he has less control.

Obama is hiking pressure on congressional Republicans on the debt ceiling and immigration, two big issues in which public sentiment and political risks seem to favor him.

His refusal to negotiate on the debt ceiling is an especially sharp departure from his usually accommodating style. Obama is gambling that Republicans will yield to fears of a ferocious public backlash if they leave the government unable to pay its bills in their push for spending cuts.

But it is a risk. Unresolved brinkmanship over the debt ceiling could lead to an economic calamity that would damage Obama’s second term and eventual legacy — not to mention Americans’ lives.

Meanwhile, outrage over the Connecticut grade school massacre forced the president to seek a gun-control package ahead of expectations. Americans have resisted significant gun-limiting bids for years, however, and the pro-gun-rights lobby remains powerful. Also, there’s less Democratic unity on this issue than on many others.

Obama’s allies already are dampening expectations on key components, including an assault weapons ban.

Vice President Joe Biden, who stood at Obama’s side as the president announced his proposals on Wednesday, said, “I have no illusions about what we’re up against or how hard the task is in front of us. ... We should do as much as we can, as quickly as we can.”

Among the second term’s top-tier issues, immigration may be the one in which Obama enjoys the most leverage. That’s a dramatic change from his first term, when it was relegated to the background.

The White House is hinting at a comprehensive bill this year that would include a path toward citizenship for millions of immigrants now in the country illegally.

Many Republicans, stung by heavy losses among Hispanic voters in the last two presidential elections, say they also want to revamp the nation’s immigration laws. But a sweeping bill with citizenship provisions is bound to draw some conservative fire. If Obama goes big, it could put GOP leaders in a bind.

A CBS News poll last month found that 47 percent of adults felt illegal immigrants working in the U.S. should be allowed to remain and eventually apply for citizenship. An additional 24 percent said they should be allowed to stay as guest workers.

The levels of support were higher than a CBS poll found 15 months earlier.

Such findings, coupled with Latino voters’ rejection of Republican candidates in 2008 and 2012, could enable Obama to drive a hard bargain on immigration if he chooses.

On the debt ceiling, he already has chosen a newly tough public posture.

Every year or so, lawmakers must raise the ceiling to enable the government to keep paying the bills Congress racks up through deficit spending. The issue became bitterly partisan in 2011, when Republicans demanded deep spending cuts and other concessions for their cooperation on the debt limit.

Obama, as part of a broader deficit-spending debate, energetically negotiated, offering spending cuts to balky Republicans. After the stare-down went to the final hour, a rating agency downgraded the nation’s creditworthiness because of the endless quarreling in Washington.

This time, Obama says he will refuse to negotiate over the debt limit. GOP lawmakers, he said at a news conference Monday, can either “act responsibly and pay America’s bills, or they can act irresponsibly, and put America through another economic crisis. But they will not collect a ransom in exchange for not crashing the American economy.”