He didn’t again compare members of Congress to his children or say reaching a budget deal involved people eating their peas.

But an exasperated-sounding President Obama on Friday employed a mix of scolding and imploring as he held his second press conference in five days to try to use public pressure to get Republicans to agree to his — or any — version of a deal that would raise the $14.3 trillion debt limit and reduce the budget deficit.

From the start of Obama’s press conference, one thing was clear: he had little to new to say on the specific policy issues that divide the two parties.

His messages were the same as they have for the past several days: Washington should use this moment for a broad deficit reduction deal, an agreement must include some tax increases, and he and Republicans could reach such a deal if partisanship were put aside.

He would not put his firm support behind a smaller agreement being written by Senate leaders Mitch McConnell (R-Ky.) and Harry Reid (D-Nev.), instead insisting Congress should still consider the broader deal he nearly reached with House Speaker John A. Boehner (R-Ohio.) that would reduce the deficit by around $4 trillion over the next decade.

But Obama made clear his frustrations with the process. He said congressional Republicans were ignoring polls that show the majority of the public, and even many Republicans, favor a deficit reduction proposal that would combine tax increases and spending cuts. He cast the debt ceiling challenge as “manufactured” by Republicans who in the past had backed increases in the federal borrowing limit without accompanying spending cuts but are refusing to do so now.

And he bluntly dismissed any consideration of a constitutional amendment that would mandate Congress balance the budget, an approach many House Republicans favor.

“We don’t need a constitutional amendment to do our jobs,” Obama said.

Obama repeatedly accused some Republicans of playing politics, even though many, particularly those aligned with the tea party movement, strongly opposed tax increases and favored spending cuts before they arrived in Washington and seem as motivated by principles as the president.

Politically, the goal of Obama’s repeated public appearances in the last few weeks is not only to move Congress toward reaching an agreement, but to show a president who approaches these problems like an “adult” in the room, a term the White House aides have used in the past to describe the president’s approach to reaching deals in partisan Washington.

What’s not clear is if all this pressure from Obama will actually influence the Republicans. Polls aside, many in the congressional GOP seem determined to avoid an agreement that cuts spending less than the estimated $2.4 trillion needed to extend the debt ceiling through November 2012. Obama, in the press conference, again rejected using spending cuts only to reach that number.

And reaching any kind of “big deal,” as Obama called a broader, $4 trillion agreement, would require tax increases that Republicans seem unlikely to adopt, no matter how often the president scolds them for taking this position.