With Senate Democrats rushing to meet a June deadline for a health care reform package, the cost of the overhaul — and who pays for it — is emerging as another serious roadblock to Republican buy-in.

Particularly in light of this week’s report on the looming insolvency of Medicare and Social Security, Republicans are skittish about creating a new government program projected to cost nearly $2 trillion over the next decade. Democrats and Republicans remain hopeful that a bipartisan deal can be reached, but neither party has figured out a politically acceptable way to pay for it.

“Costs are definitely the gorilla in the room,— said Sen. Mike Enzi (R-Wyo.), the ranking member on the Health, Education, Labor and Pensions Committee. “There are a lot of plans out there. Some of them I think are ridiculous; some of them I think might work.—

The Finance and HELP committees are holding a series of working groups this month to try to reach an agreement on the policies and costs of health care reform. A bill is scheduled to be marked up in June, and there are tentative plans for a late July floor vote.

Democratic and Republican Senators generally agree on the need for an overhaul, and want to pass legislation in the near term. Sens. Enzi, Judd Gregg (N.H.) and Orrin Hatch (Utah), who along with Finance ranking member Chuck Grassley (Iowa) are the key Republican negotiators, all said this week that they are optimistic about reaching a bipartisan deal.

By all accounts, the biggest sticking point on a health reform agreement is whether the package should include a government-run insurance option, commonly referred to as a “public plan.— But coming in at a close second is the issue of how to pay for a sweeping plan.

“It’s a big issue no matter what, because it’s a huge amount of money — huge,— Democratic Conference Vice Chairman Charles Schumer (N.Y.) said. “And yet, if you ask the American people, this is one place they really want to see things happen. So, we’re looking and checking out everything.—

“There are a lot of differences right now on health care, and nobody’s really pulled it all together,— Hatch added. “We’re working hard to try and find a way of pulling it together and still make it something that works.—

Complicating matters, the trustees for Social Security and Medicare revealed this week that the programs will run out of money earlier than expected. In response, Republican leaders renewed previous demands that health care focus on overhauling the two existing entitlement programs. Democrats, conversely, argued that the report shows that a major health care overhaul can maintain the solvency of Medicare and Social Security.

Absent substantial budget cuts to free up revenue, President Barack Obama and Congressional leaders are likely going to have to agree on tax increases to fund health care reform. And a knowledgeable Democratic Senate aide said the fight over how to cover the costs, and who foots the bill, will be moot if Democrats and Republicans fail to compromise on the public plan issue.

With that in mind, Democratic leaders are leaving open the possibility of pressing ahead with a partisan bill under reconciliation, which would allow the legislation to pass with just 51 votes.

Giving hope that a widespread agreement can be reached, however, a group of key health care groups came together this week to announce they would cut $2 trillion in health care costs over the next 10 years. Many saw the move as a signal that health care reform is possible this year.

But the health care industry’s willingness to engage is likely to stop short of agreeing to pay a tax to fund reform. Among the plans bandied about is one that would require businesses to provide health insurance to employees or pay a tax to help Washington pick up the slack.

Another source of potential revenue involves ending the “exclusion— benefit given to workers who receive employer-paid health coverage.

Some Republicans have actually shown an interest in taxing employer-provided health coverage as regular income, including Sen. John McCain (Ariz.), who advocated for it during his White House bid last year. But Obama criticized McCain for the proposal, and is unlikely to agree to it now. Organized labor is also likely to resist the idea, as many union workers received expensive, gold-plated health coverage.

“Now that Obama is stuck, we don’t have any incentive to help him out of that trap,— a Republican Senate aide said.