The first federal government shutdown in more than 15 years drew closer Tuesday as President Obama and congressional leaders failed to make progress on a budget for 2011 after back-to-back meetings at the White House and on Capitol Hill.

Obama and Congress remained billions of dollars apart and at odds over where to find savings after an 80-minute West Wing meeting that included House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Harry M. Reid (D-Nev.). In the meeting, Boehner floated the possibility that he may seek as much as $40 billion in cuts, $7 billion more than the two sides have been discussing for the past week.

Growing irked by the prolonged negotiations, Obama demanded that the congressional leaders “act like grown-ups.”

“If they can’t sort it out, then I want them back here tomorrow. And if that doesn’t work, we’ll invite them again the day after that,” Obama told reporters in a rare appearance in the press room, hours after the meeting.

The president invited congressional leaders back to the White House on Wednesday, but he is scheduled to spend much of the day traveling and, as of late Tuesday, no meeting had been finalized.

Boehner, who watched Obama’s remarks in his Capitol suites, pledged to keep talking. His aides deflected reports that the speaker is setting a new target of $40 billion in cuts, but he also rejected the $33 billion figure that Republican leaders in the House and Democratic leaders in the Senate had been working toward.

“There was no agreement, so those conversations will continue. We made clear that we’re fighting for the largest spending cuts possible,” Boehner told reporters moments after Obama spoke.

Reid continued to accuse Republicans of not being “fair and reasonable” in their demands for higher cuts and specific changes to social and regulatory policies. Asked if he would be willing to reach $40 billion in cuts, however, Reid demurred.

“I’m not negotiating here what we’re going to do ultimately,” he told reporters.

A late-day meeting between Boehner and Reid in the speaker’s office produced no breakthroughs, but aides to both lawmakers issued identical statements calling it “a productive discussion” — a significant shift in tone after a week in which the two traded accusations across the Capitol.

Reid closed the Senate chamber Tuesday evening with an optimistic speech describing “good faith” talks that are “not that far apart.”

“The government is not going to shut down — yet. There’s still air in the tire; at least we still have some miles to travel. I hope we have enough air in the tire to get us where we need to go,” he said.

A few days left

Without any resolution — either through a full spending plan or another short-term extension — the federal government would shut down at midnight Friday, with the full impact coming when the workweek resumes Monday.

Many of the most immediate effects of a shutdown would be felt in Washington, where the Smithsonian museums and other tourist sites would close, keeping as many as 500,000 visitors locked out of the city’s main attractions, according to senior government officials. If the impasse continues until Monday, a slew of other services would be halted, including the processing of tax refunds.

Aside from agreeing on how much to cut, two key stumbling blocks remain. One is a demand by Democrats to include roughly $10 billion in one-time cuts from programs such as Pell grants and farm subsidies. Republicans have rejected those cuts because they wouldn’t be permanent. On Tuesday, Boehner called such proposals “smoke and mirrors.”

Republicans cited the suggested cuts to rebut Obama’s oft-repeated claim that he has met the GOP “more than halfway” to its goal of cutting $61 billion from the government. Obama rejected that outlook Tuesday, calling his proposed Pell grant reductions “real cuts.”

Another impediment to a deal is Boehner’s insistence on attaching what are known as policy riders to the legislation. One such provision, approved as an amendment to the House bill in February, would keep open a mountain repository outside Las Vegas for storage of high-level nuclear waste — a plan Reid absolutely opposes for his state.

Political consequences

White House officials privately acknowledged that they have become wary of the political consequences of the spending battle, in part because a shutdown would reinforce the notion for many voters that leaders in Washington are unable to resolve key issues.

At the same time, White House officials are reluctant to agree to proposals that would inflame Obama’s liberal base, especially during the same week that the president launched his reelection campaign with a direct appeal to core supporters who provided the energy for his 2008 bid.

Boehner has struggled with his own political base, most prominently the tea party activists who propelled the major Republican victories in the 2010 midterm elections. Some of the 87 Republican freshmen who benefited from tea party support have resisted any compromise to their campaign pledge to slash spending to 2008 levels.

Many freshmen, however, are open to some form of compromise, though they aren’t sure about the right mix of spending cuts and policy riders. At this late stage, Boehner still has not sought input from the freshmen about where they would make deals, they said.

Instead of directly seeking their support for a specific plan, Boehner has made it clear that some kind of compromise is necessary, according to Rep. Kevin Yoder (R-Kan.), who said the speaker has encouraged the freshmen to “fight the battle on the highest ground possible.”

Yoder rejected the idea of “let’s shut down the government as a means to an end,” because at some point, he noted, the Republican-led House and the Democratic-led Senate will have to govern before the 2012 elections.

“Either the government shuts down until January 2013 [when a new Congress will arrive], or someday, there’s going to be a compromise,” he said.

Staff writers David Fahrenthold, Ed O’Keefe, Philip Rucker, Debbi Wilgoren and Felicia Sonmez contributed to this report.