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Democrats said they would prefer spending levels tens of billions of dollars higher and that they already have compromised by accepting the lower number.

Mr. Obama’s decision to call congressional leaders to the White House marks a major shift. Until that point, he was content to let congressional leaders do the fighting.

By directing the top Democrat and top Republican in each chamber to come to the White House, he has invested himself deeply.

House Minority Leader Nancy Pelosi, California Democrat, called the meeting “worthwhile,” and Mr. Boehner said it was “polite.” Still, it was clear that Mr. Obama was no more ready to negotiate than the four congressional leaders.

Democrats insist that if the House votes on the Senate version, it would pass.

Indeed, Democrats have identified at least 17 Republicans who have said they would vote for the “clean” Senate legislation if given the chance. That number, combined with all Democrats, would ensure the bill’s passage.

Republicans had to use parliamentary tactics to keep Democrats from being able to offer the Senate version on the House floor Wednesday.

“Why is the majority afraid of democracy? Why are they afraid of allowing this House to work its will?” said Rep. Chris Van Hollen, the Maryland Democrat who tried to force a vote on the Senate measure.

Republicans countered that while there isn’t agreement on every part of the overall spending bill, Congress could approve funding for programs where there is unity — such as veterans’ benefits, paychecks for the National Guard and reopening the national parks.

Park closures in the Washington area have become a thorny problem for the White House after elderly veterans had to push through barricades to get into the National World War II Memorial on the Mall on Tuesday.

House Republicans on Wednesday opened an official investigation into the park service’s handling of the shutdown.

In a letter to park service, Director Jonathan Jarvis, Rep. Doc Hastings, Washington Republican and chairman of the House Natural Resources Committee, questioned why the service suddenly posted guards and barricades at an open-air site that under normal circumstances isn’t guarded for at least 10 hours out of the day.

The park service reversed itself Wednesday and said it would permit some veterans groups to visit the memorial.

Mr. Hastings said he wanted to know whether the White House pressured the park service to close high-profile sites — particularly since the Lincoln Memorial wasn’t closed during the last government shutdown in 1996.

Seth McLaughlin contributed to this report.