From a just released ABC/Washington Post poll, Most Back Cuts Overall – But Not to the Military:

For all the dire warnings, most Americans welcome a five percent cut in overall federal spending this year. But the defense budget is another matter.

The public by nearly 2-1, 61-33 percent, supports cutting the overall budget along the lines of the sequester that took effect last Friday. But by nearly an identical margin, Americans in this ABC News/Washington Post poll oppose an eight percent across-the-board cut in military spending.

See PDF with full results, charts and tables here.

The best evidence this poll is bad news for Obama is the reaction:

Why should we, the sequester cuts — other than the military — are working out fine so far, and there will be bipartisan agreement to give the military more flexibility.