In announcing their shift on the payroll tax issue Monday, Boehner and two other top House GOP leaders said they wanted separate the matter from legislation dealing with unemployment benefits and the doc fix.

Doing so would "protect small businesses and our economy from the consequences of Washington Democrats' political games," said Boehner, Cantor and House Majority Whip Kevin McCarthy, R-California.

Schiller told CNN the idea of divorcing the payroll tax cut from an unemployment benefits extension and the doc fix was a "clever" idea on the part of the House GOP leadership.

Doing so would have removed the Democrats' "leverage on the other issues of unemployment and Medicare payments," she said. "Also, as the unemployment numbers get better, the rationale for a lengthy extension of benefits diminishes. The longer the GOP can stall on the unemployment extension, the more likely it is they win in terms of authorizing a much shorter extension than the Democrats would like."

Democrats, however, quickly pushed back hard against the idea.

Senate Majority Leader Harry Reid, D-Nevada, and House Minority Leader Nancy Pelosi, D-California, on Tuesday urged Republicans to allow Congress to quickly complete its work on all three issues -- the payroll tax cut, unemployment insurance, and the doc fix.

Pelosi said Congress should cancel a recess currently scheduled for next week if it fails to complete work on all of them by Friday.

"These crucial policies affect millions of middle class families and seniors and must not expire at the end of this month," Pelosi said.

Instead of a separate measure involving only the payroll tax cut extension, the tentative agreement Tuesday was a more comprehensive package worked out by the conference committee negotiators

It remains unclear if the increasingly conservative House GOP caucus will be willing to go along with the tentative deal. House Republican freshmen, elected on a tidal wave of tea party support in 2010, have made deficit reduction their top priority and repeatedly insisted that any new initiatives be fully paid for.

Rep. Dennis Ross, R-Florida, said discussion Tuesday night in the House Republican caucus was "heated" over not paying for the payroll tax cut extension, which he called "bad policy," while fellow Floridian Rep. Allen West, a tea party conservative, said "this doesn't look like a good deal to me."

Meanwhile, two New York Republicans, Reps. Tom Reed and Peter King, sounded more supportive, with King saying he expected the measure to pass.

One key conservative, Rep. Jim Jordan of Ohio, indicated Tuesday he's prepared to back Boehner and the other House GOP leaders.

Jordan's "view is anytime we're letting people keep more of their money, that's a good thing," said Brian Straessle, a spokesman for the Republican congressman.

Veteran political analyst Norm Ornstein warned that the GOP leadership's repeated maneuvering on the issue could end up backfiring.

House Republican leaders have been "trying to make the best of crummy situation," Ornstein told CNN. But tea party Republicans "don't care" if fighting the tax cut extension is "a political loser. They don't like the payroll tax cut and now the (leadership's) sin is being compounded by saying they won't pay for it."

This "could play out in ways that make the life of Boehner (and other Republican leaders) a little less comfortable," he predicted.