Washington ? Prodded by an insistent President Barack Obama, Congress’ top two lawmakers sought to reinvigorate compromise talks Tuesday aimed at cutting tens of billions in federal spending and averting a partial government shutdown Friday at midnight.

There was at least a hint of flexibility, accompanied by sharply partisan attacks and an outburst of shutdown brinksmanship.

According to Democrats, House Speaker John Boehner, R-Ohio, suggested at a White House meeting that fellow Republicans might be able to accept a deal with $40 billion in cuts. That’s more than negotiators had been eyeing but less than the House seeks.

The speaker’s office declined comment, and Boehner issued a statement saying, “We can still avoid a shutdown, but Democrats are going to need to get serious about cutting spending — and soon.”

For his part, Senate Majority leader Harry Reid sounded an accusatory note. “I hope the Republicans do what the country needs, not what they believe the tea party wants,” he said at the Capitol.

“I mean, it seems that every step we take, it’s something just to poke us in the eye,” he said.

Boehner and Reid met privately later in the day. While there was no indication of substantive progress, there was a marked change in tone afterward.

Spokesmen for the two issued identical statements, shorn of partisan bickering, saying the two leaders “had a productive discussion. They agreed to continue working on a budget solution.”

Obama stepped forcefully into the dispute, at times sounding like an exasperated parent.

He convened a meeting at the White House with the chief congressional antagonists, rejected a Republican proposal for an interim bill with sharp cuts and then announced Boehner and Reid would meet later in the day.

If they can’t sort out their differences, he said, “I want them back here tomorrow.”

And if that doesn’t work, he added, “we’ll invite them again the day after that. And I will have my entire team available to work through the details of getting a deal done.”

Obama, eager to regain the confidence of independent voters as he seeks a new term, said the American public expects that its leaders “act like grown-ups, and when we are in negotiations like this, that everybody gives a little bit, compromises a little bit in order to do the people’s business.”

At issue is legislation needed to keep the government running through the Sept. 30 end of the budget year, and a desire by all sides to avoid being blamed politically if there is a shutdown.