Sen. Chuck Schumer, D-N.Y., also said an announcement by House Republicans that they plan to approve a short-term increase in the nation's borrowing limit without demanding spending cuts was "positive step." He added, though, the extension should be longer than the three months they have outlined.
"We don't want to play fiscal cliff every three months," Schumer said.
Republicans in recent days have backed away from their insistence that they would not increase the nation's borrowing limit -- known as the debt ceiling -- without deep spending concessions. If the new proposal holds, the shift would clear the way for Congress to avoid a potential government default this spring.
But GOP officials insist that they will not move unless Senate Democrats give them the debate over the federal budget they have been denied for years.
"All of us losing our pay if we don't pass a budget is the right thing to do," said Sen. Roy Blunt of Missouri, vice chair of the Senate Republican Conference.
Sen. Ted Cruz, a Texas Republican and a favorite of tea partyers, said he supports the strategy from his party's leaders in the House.
"There is no doubt the Senate hadn't done its job," said Cruz, who was elected to his first term in November. "It's been nearly four years since it's passed a budget. And the Senate should pass a budget."
The Senate Republicans will get a budget from the Democrats, Schumer said.
"We Democrats have always intended to do a budget this year," Schumer said, adding the Democrats' budget would raise taxes while offering overhauls to the tax code likely to find Republican support.
"We're going to do a budget this year and it's going to have revenues in it. And our Republican colleagues better get used to that fact," Schumer added hours before President Barack Obama began his second term, which officially began at noon Sunday and will be heralded with celebrations around the capital city a day later.
The White House, too, said it remained committed to what officials called a "balanced" approach to cutting the nation's $16.4 trillion nation debt. Asked by ABC's George Stephanopolous whether Obama "will only sign a budget deal if it includes new revenues," White House senior adviser David Plouffe agreed.
"Yes, it's got to be balanced," said Plouffe, who expects to leave his first-floor West Wing office soon. "We need spending cuts, entitlement reform and revenue. We have to have that."
Plouffe said the new Republican strategy reflects a weak opposition after November's election that gave Obama a second term.
"This is a big departure for them, you know?" Plouffe said of Republican lawmakers' change of course.
House Republican leaders on Friday offered Obama a three-month increase to the nation's credit card and a dodge to a looming, market-rattling debt crisis. They backed off demands that any immediate extension of the government's borrowing authority be accompanied by stiff spending cuts.
They also added a caveat designed to prod Senate Democrats to pass a budget: no pay for lawmakers if there again is no budget passed this year. House Republicans have passed budgets for two consecutive years; the Democratic-controlled Senate last passed a complete budget in 2009.
Plouffe said the three-month extension "is no way to run an economy or a railroad or anything else" and seemed cool on the GOP's short-term proposal. Yet he said Obama would review Republicans' ideas.
"We haven't seen what they're proposing, and they're going to have to pass it," he said, hinting at House Speaker John Boehner's difficulty in rounding up enough votes within his caucus to pass his own party's proposals.
Schumer and Cruz spoke with NBC's "Meet the Press." Blunt spoke to "Fox News Sunday." Plouffe appeared on CNN's "State of the Union," "ABC's "This Week" and CBS' "Face the Nation."
No House Republicans appeared on the networks' Sunday morning talk shows to represent their proposal.
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