A Washington Post poll published today contains, at best, marginally good news for President Obama and the Democrats. At worse, it suggests that the president may have engaged too late on the budget fight.

Democrats had hoped that if the government shut down, Republicans would bear the blame. And considering how much ground Democrats have already given, Republicans should get the blame if they don’t take the deal that Obama has put forward through the Senate Budget Committee in ongoing negotiations. (Whatever Speaker John Boehner may say, those negotiations have been active and ongoing.)

Instead, the public is split evenly — 37-37 percent — in apportioning blame for a shutdown.  Not surprisingly, Republicans would blame the Democrats and Democrats would blame the Republicans. The key is that independents are pretty well split down the middle. As The Post reported, 35 percent of independents say they would blame Obama for a shutdown; 34 percent would blame the GOP.

 Obama’s lieutenants counted on the public seeing the Republicans playing politics with the shutdown — and, the public does see things that way. According to the Post poll, 62 percent say the Republicans are playing politics with the shutdown, compared with only 31 percent who say the GOP is trying to resolve the issue.  Obama’s numbers are better, but not by that much. The survey found 51 percent saying Obama is playing politics, compared with 43 percent who say he’s trying to resolve the issue.

If the Obama strategy were working as it were supposed to, Obama’s positive number on that question would be much higher.  As it is, he has made enormous concessions to the Republicans without getting much back from them — and without getting much credit from the public.

 Perhaps Obama will turn things around with today’s White House meeting, and over the next few days. But it’s hard to win a game in the 10th inning if you fall too far behind in the ninth. The president has a lot of work to do, and the Republicans are faring better than the president expected — and better than they deserve to, given their public intransigence.