U.S. President Barack Obama, right, meets with congressional leaders including House Speaker John Boehner, a Republican from Ohio, second from right, House Minority Leader Nancy Pelosi, a Democrat from California, and House Majority Leader Eric Cantor, a Republican from Virginia, in the Cabinet Room of the White House in Washington, D.C., U.S., on Thursday, July 7, 2011. (Photographer: Andrew Harrer/Bloomberg

For months Democratic strategists have pointed to the House vote in favor of a budget proposal put forward by Wisconsin Rep. Paul Ryan that would transform Medicare into a voucher program as their silver bullet heading into the 2012 congressional election.

“Our three most important issues: Medicare, Medicare and Medicare,” House Minority Leader Nancy Pelosi (Calif.) said recently when asked how her party could reclaim the majority in 2012.

So, might Obama’s decision to put Medicare on the table rob his party of a prized political issue heading into the next election? There’s an active debate within the party on that very question.

Democratic strategists are cautiously optimistic that such a scenario won’t come to pass, insisting that making changes to strengthen Medicare — if that comes to pass — is a very different thing from what they describe as a drastic overhaul of the program being proposed by Ryan.

“The fundamental contrast is between Democrats eager to see Medicare succeed and the GOP who want to dismantle Medicare entirely,” said J.B. Poersch, a former executive director at the Democratic Senatorial Campaign Committee. “That contrast isn’t going away.”

Other Democrats point out that most of the party’s pickup chances in House races lie with challenger candidates so any vote on a grand bargain including Medicare cuts would not likely negatively impact them since they wouldn’t have to vote on it.

(The Cook Political Report’s latest House race rankings shows 18 Democratic incumbents in potentially competitive races as compared to 23 Republicans.)

But, there is another significant strain within the Democratic political professional class who believe any changes to Medicare in a debt ceiling deadline deal would force the party to give up the high ground they currently hold on the issue.

The thinking among that group is that voters won’t delve deeply enough into the specifics of the Medicare proposals to differentiate between what the Obama White House wants and what Ryan pushed.

“A grand bargain on Medicare will let Republicans who support the deal off the hook on their Ryan budget vote,” said one senior Democratic operative granted anonymity to speak candidly about strategy. “If attacked on the Ryan budget they can easily counter they voted for the same thing Obama supported. Poof.”

No matter where you come down on this particular debate, it does highlight an important political reality: what’s good for the president is not always what’s good for his party in the House and Senate.

As we noted yesterday, a big compromise on the debt would considerably strengthen President Obama’s hand heading into 2012.

The Obama re-election campaign has been — and will continue to be — heavily focused on independents= voters who respond well to the image of a president willing to rise above petty partisanship to compromise for the good of the American people.

It’s not clear that such a large-scale compromise would be anywhere near as beneficial politically for Democrats in House and Senate races — particularly if you believe the argument that such a deal either takes Medicare off the table entirely or, at the least, dilutes its impact with voters.

“Many Democrats in the House and Senate already feel [Obama] has been looking out for his own political agenda at their expense,” said one high level Democratic operative involved in downballot contests. “They already feel that they sacrificed seats in the 2010 election for him. Not many will be willing to do so again in 2012 if he deals the Medicare card away too.”

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