Big majorities of Democrats, Republicans and independents believe that the sequester will hurt the economy and the military. But a newly released Washington Post-ABC News poll reveals that no proposed solutions to the sequester (of five tested) rallies majority support across party lines.

That's the conundrum facing Obama and Congress as they search for a replacement for across-the-board cuts that both parties blamed each other for causing. Fully two-thirds of Americans want lawmakers to work to stop the cuts from continuing, but there's much less consensus about what to replace them with.

In addition to the economy and military, over half of Republicans, Democrats and independents predict the cuts will hinder the government's ability to provide basic services.  Just under half of each group believes their personal finances will take a hit.

The partisan agreement is striking given that Obama and Democrats made far more dire predictions than Republicans of the sequester's consequences as the deadline approached.

But when asked about five possible replacements for the sequester, there is less agreement. On two of five proposals, majorities agree to say no: Most Democrats and Republicans oppose cutting Medicaid and raising the Medicare retirement age from 65 to 67. But while most Democrats support targeted military cuts and paring back tax deductions for the higher-income individuals and businesses, fewer than half of Republicans back them. Political independents support targeted military cuts and limiting tax deductions for the wealthy.

The lack of bipartisan enthusiasm for key sequester replacements helps explain why the automatic cuts began in the first place - both party's leaders agreed they should not occur. But with no popular replacements apparent, a compromise proved elusive.

It's unclear whether or how Obama and Congress will replace the cuts now in effect, but to do so may require expanding the policy playing field or risking blowback from at least one party's constituency. At a time when both Obama and Congress are at a low ebb in popularity, taking the latter route could be a heavy lift.

The Post-ABC poll was conducted March 7-10, 2013 among a random national sample of 1,001 adults interviewed on conventional and cellular phones. The margin of sampling error for the overall results is 3.5 percentage points.

Post-ABC poll full results and interactive group breakdowns from the Post-ABC poll.

Capital Insight polling director Jon Cohen and pollsters Peyton M. Craighill and Kimberly N. Hines contributed to this report.