WASHINGTON – Even if President Obama succeeds in getting Republicans to agree to tax increases on the wealthy as part of a “fiscal cliff” deal, the country’s grim budget realities will still cast a long shadow — limiting his ambitions as he begins plotting a second-term agenda.

Any agreement is likely to result in less than the $1.6 trillion in new taxes over the next decade that Obama requested in his initial offer to House Republicans, and White House aides are signaling to allies that any new money from taxes would be used almost entirely for deficit reduction — not for ambitious new spending programs or government expansions.

Where Obama entered office four years ago planning to seize a moment of economic crisis as an opportunity for transformational policies such as the $800 billion stimulus and his health care overhaul, he begins his second four years with few, if any, similarly expansive or costly prospects.

Instead, any new spending programs will, by necessity, be small and narrow in scope: repairs to roads and bridges, airport renovations and other infrastructure upgrades, for example, or modest grants to help blighted city neighborhoods.

Allies expect Obama to harness the combined political capital of his reelection and the outcome of the tax fight for an aggressive push to legalize millions of illegal immigrants in what could be a signature domestic achievement.

But beyond that, the second-term agenda remains shrouded in uncertainty, with questions about whether he would pursue other politically charged issues such as climate change or voting rights.

How high Obama can aim will depend at least in part on the details of whatever deal he manages to strike in the coming weeks with House Speaker John A. Boehner, R-Ohio.

Democrats say that breaking down Republican orthodoxy on taxes would be a game-changing moment, weakening the tea party movement’s two-year stranglehold on Republican leaders and thereby paving the way for future deals.

“A good agreement could provide important momentum for the president to accomplish other items on his agenda, like immigration reform, like some energy and infrastructure initiatives,” said Rep. Chris Van Hollen, D-Md., senior Democrat on the House Budget Committee.

“The question is, what does a ‘good agreement’ mean?” Van Hollen said.

Sen. Richard Durbin, D-Ill., said Obama’s potential success over the next four years also depends on the president’s ability in the current talks to neutralize GOP threats to use votes on increasing the country’s borrowing limit to force additional spending cuts.

If the debt limit threats continue beyond this month, Durbin said, “there’s no way the president can function or this economy can grow under those circumstances.”

Republicans argue the debt limit votes are their only leverage to curb excessive federal spending. They also have issued warnings in recent days that Obama’s apparent refusal to budge on taxes threatens to damage any hopes of resetting bipartisan relations in his second term.