Senate Republicans scrambled Tuesday to avoid the ire of AARP and veterans, offering to support payments to 20 million low- income seniors and 250,000 disabled vets left out of the House stimulus package, while hoping to hold the line against unemployment insurance, energy tax breaks and other goodies backed by Senate Democrats and the Finance Committee.

Democratic leaders vowed not to allow Republicans to cherry-pick which provisions of the committee package they would filibuster and which they would accept, with Majority Leader Harry Reid (D-Nev.) saying it is a take-it-or-leave-it proposition.

“I don’t think it’s right to pick and choose,” he said. “It’s up to them to make a decision. The American people are watching.”

Reid moved Tuesday night to limit debate on a slightly modified version of the committee bill, with a cloture vote set for this afternoon.

Republicans are convinced that Reid’s bluster is all bluff, and they say he will be forced to allow amendments adding seniors and veterans once the GOP shows it has the votes to block the committee package as a whole.

Reid bristled at the accusation he was bluffing.

“If they think this is a bluff, let’s wait until we have a vote,” Reid said. “I’m not much of a bluffer.”

Reid last week had telegraphed plans to scale back the committee package if it failed to get 60 votes and drop provisions like unemployment insurance that are opposed by the GOP, but he said that new figures showing a loss of jobs in January and strong support from across the country for extending unemployment benefits changed the equation.

Finance Chairman Max Baucus (D-Mont.) also pushed the plan for a single vote on his package, with AARP’s blessing Tuesday. “There’s going to be one vote and it’s going to be the vote on the Finance Committee package,” Baucus said. “I think it’s pretty clear there will be enough” votes to pass the package, Baucus predicted. “I don’t think they want to filibuster seniors.”

Reid spoke after Sen. Ted Stevens (R-Alaska) and Minority Leader Mitch McConnell (R-Ky.) said they were working on an amendment that would add the seniors and the disabled veterans to the nearly $150 billion House-brokered package but keep the overall cost the same by shrinking the size of each check.

Stevens said he originally backed just passing the House bill but has been convinced that seniors and disabled veterans deserve checks too.

But Stevens said the overall size of the package should not increase so as not to add even more to the deficit, and he bristled at Reid’s ultimatum.

“I’m tired of that ‘take it or leave it’ … from people who don’t have the votes to begin with,” Stevens said. “The public ought to get tired of this constant posturing on what we’re going to do. We ought to get down to doing something.”

Meanwhile, the shift in the Republican message from one of simply passing the House bill last week came as lobbying groups poured on the pressure, led by AARP, which released a poll showing 90 percent support for including seniors in the stimulus package.

Sen. John Cornyn (R-Texas) acknowledged that the calculus had shifted. “I think our leaders know how to count,” he said.

The brinkmanship comes with pressure mounting on both parties to pass a package this week, as the stock market slumped again Tuesday. At his press conference, McConnell sought to downplay the daily machinations and emphasized that he thought a stimulus package would pass with broad bipartisan support.

Reid and other Democratic leaders have targeted a handful of Republicans in recent days in the hope of peeling off several wavering members of the GOP to back the bill, Democrats said, but with little apparent success.

Democrats have reportedly targeted Alaska Sens. Lisa Murkowski and Stevens, as well as Sens. Dick Lugar (Ind.), Arlen Specter (Pa.), Mel Martinez (Fla.), John Warner (Va.), Lindsey Graham (S.C.) and George Voinovich (Ohio) to join Finance ranking member Chuck Grassley (Iowa), his fellow committee members Olympia Snowe (Maine) and Gordon Smith (Ore.) and Sens. Norm Coleman (Minn.), Elizabeth Dole (N.C.) and Susan Collins (Maine), who Democrats believe will support cloture this week. Additionally, Environment and Public Works ranking member James Inhofe (R-Okla.) has also been rumored to be a potential target for Democrats because of his ties to the home builders.

But by Tuesday afternoon, several of those Members appeared to no longer be in play, including Stevens and Warner, who told reporters he would not vote for cloture. Stevens’ exit from the list of potentials also would likely dim Democrats’ chances to sway his fellow Alaskan Murkowski, who would be loath to vote against him when he is facing a difficult re-election bid. Voinovich is also reportedly no longer an option, Republicans said, and most dismissed the possibility that Graham — a vocal backer of GOP presidential hopeful Sen. John McCain (Ariz.) — would vote for a bill McCain would oppose.

Similarly, Inhofe appears to be firmly in the GOP camp, Democrats and Republicans alike said.

Snowe, who voted for the Finance Committee package and challenged Treasury Secretary Henry Paulson on Tuesday to back unemployment benefits, expressed frustration at the gridlock.

“It’s unbelievable that we can’t come together on both sides and get it done,” she said, arguing that adding money for unemployment insurance, disabled veterans and seniors is “the right things to do.”

But she held out hope that the two sides could reach a deal.

“There should be a way to agree on what will be in the amendment tree. Both sides are having some challenges, to say the least,” she said.