Talks appear to be intensifying on Capitol Hill on reaching a deal on long-overdue legislation to finance the government through the end of September — and avoid a government shutdown. Whether a shutdown can be avoided in three days’ time is another matter.

A White House meeting Tuesday that included President Barack Obama, House Speaker John Boehner, R-Ohio, and Senate Majority Leader Harry Reid, D-Nev., failed to produce the hoped-for breakthrough, however, with a stopgap government funding bill set to expire Friday at midnight.

Obama ratcheted up the pressure afterward, sounding exasperated with Republicans for not warming to a White House proposal that matched, more or less, an earlier GOP framework proposed in February. In it, Democrats propose cuts netting $73 billion in savings below Obama’s original requests — or $33 billion below current spending levels.

Boehner said yet again that there is no agreement on a level of spending cuts. And there’s been little progress on the 50-plus GOP policy “riders” dotting the House version of the measure.

“There’s no reason why we should not get an agreement,” Obama said. “We have now matched the number that the speaker originally sought. The only question is whether politics or ideology are going to get in the way of preventing a government shutdown.”

Talks also took place Tuesday between Boehner and Reid at the Capitol, with both sides reporting a productive discussion.

All sides say they don’t want a partial shutdown of government agencies that would close national parks, shutter passport offices and turn off the IRS taxpayer information hot line just a week before the April 18 filing deadline. But numerous other essential federal workers would stay on the job, including the military, FBI agents and Coast Guard workers. Social Security payments would still go out and the mail would be delivered.

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

According to Democratic and Republican officials, Boehner suggested at the 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 to 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.”

Obama took his most forceful steps yet in trying to prod the stalled talks. He called the White House meeting, rejected a Republican proposal for an interim bill pairing additional spending cuts with a one-week plan to keep the government open, and then announced that Boehner and Reid would meet later in the day.

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

At issue is legislation needed to keep the day-to-day operations of federal agencies going through the Sept. 30 end of the budget year. A Democratic-led Congress failed to complete the must-pass spending bills last year. Republicans stormed into power in the House in January and passed a measure with $61 billion in cuts that even some GOP appropriators saw as unworkable. It was rejected in the Democratic-controlled Senate.

Republicans also have added dozens of policy provisions concerning hot-button topics like abortion, global warming and the environment, and Obama’s health care law. Those appear as troublesome as finding agreement on what and how much to cut from agency budgets.

“What we can’t be doing is using last year’s budget process to have arguments about abortion, to have arguments about the Environmental Protection Agency, to try to use this budget negotiation as a vehicle for every ideological or political difference between the two parties,” Obama said.

Democrats said Boehner eventually would have to part company with tea party-backed lawmakers who propelled Republicans to power, and they accused him of reneging on an agreement to cut $33 billion, increasing the chances of a shutdown.

In return, Republicans accused Democrats of resorting to budget gimmicks to make it look like they favored deep cuts, when in fact they were finding ways to ease the potential pain.

Twin partial closures in the mid-1990s boomeranged on Republicans when Newt Gingrich was speaker, helping President Bill Clinton win re-election in 1996.

This time, it’s Obama who is exuding confidence as Boehner seems hemmed in by his hard-charging class of 87 freshmen, many of whom won office with backing from tea party purists.

On Monday, Boehner informed rank-and-file Republicans he would seek passage of a new stopgap bill, a weeklong measure that includes $12 billion in cuts and funds the Defense Department through the end of the year.

Obama rejected it. He said he would sign an interim bill only if one were needed to get the paperwork together on a broader agreement and pass it through both houses.

Meanwhile, 16 moderate Senate Democrats sent Boehner a letter urging against a shutdown that could harm the economy and instill hard feelings that would harm the chances of bipartisan cooperation on long-term fiscal challenges.