The move by McConnell, R-Ky., prevented the Senate from voting on the GOP plan to extend the payroll tax cut, which passed the House Tuesday.
Senate Majority Leader Harry Reid, D-Nev., said earlier the payroll tax bill, crafted by House Republicans, "is dead on arrival in the Senate."
Democrats have withheld support for the omnibus spending bill in the hopes of getting House Speaker John Boehner, R-Ohio, to agree to changes in the payroll tax bill, Politico reported.
"There's agreement on the funding bill, but no agreement and no plan at all about how we're going to pass the payroll tax cut extension," McConnell said Wednesday during a heated exchange with Reid. "We ought to finish our most immediate concern first."
"As soon as we put this useless partisan charade behind us, we can negotiate a solution that protects middle-class workers," Reid said.
White House Communications Director Dan Pfeiffer issued a statement Wednesday saying President Barack Obama "continues to have significant concerns about a number of provisions that have been reported to be in the Republican agreement on the omnibus."
"This includes provisions that would undermine Wall Street reforms, enact extreme social and ideological riders, undercut environmental protections, and threaten the foreign policy prerogatives of the president," Pfeiffer said. "Given the magnitude of the legislation -- providing over $1 trillion dollars in funding -- coupled with the unresolved payroll tax cut and unemployment insurance extension, Congress should pass a short-term continuing resolution as it has seven times already this year so that all parties have an appropriate opportunity to consider and complete all of the critical budget and economic issues necessary to finish our responsibilities for the year."
The House voted 234-to-193 Tuesday to pass the Republican payroll tax-cut extension. The plan links the extension to a host of other measures -- including a provision to speed up a decision by the Obama administration on building the Keystone XL oil sands pipeline system to transport synthetic crude oil and diluted asphalt, tar and other road- and roof-surfacing materials to the Gulf Coast from Alberta, Canada -- a project the White House has sought to delay.
It includes provisions to roll back Environmental Protection Agency rules limiting toxic air pollutants from commercial and industrial boilers, and ban the EPA from proposing a new standard in the near future. It would extend unemployment insurance but cut the maximum unemployment coverage to 59 weeks from the current 99 weeks by mid-2012. And it would prevent a 27 percent cut in Medicare reimbursements to doctors next year -- instead, increasing their Medicare payments 1 percent each of the next two years.
The plan seeks to pay for the extended tax cut and added unemployment benefits by cutting back on social-program benefits, selling federal assets, freezing federal employees' pay through 2015 and cutting the number of federal workers by about 10 percent through attrition.
The vote on the bill generally followed party lines, but 14 Republicans voted against it and 10 Democrats voted for it -- each defying the wishes of their party leadership.
Reid said Tuesday the bill was "a pointless partisan exercise."
"The bill is dead on arrival in the Senate," he said. "It was dead before it got to the Senate."
McConnell said Reid and other Democrats were siding with environmentalists over "job creators."
"It's time for the Unites States Senate to act, and they're going to act, because we can sit here and stare at each other in the face for as long as it takes, but they are going to act," The Hill reported Boehner said Wednesday.
A Senate rejection would set the stage for House and Senate compromise negotiations that were likely to continue into the weekend, aides said.
President Barack Obama said last week he would reject any effort to tie the oil pipeline to the payroll tax cut.
In its veto threat Tuesday, the White House said House Republicans were protecting tax breaks for the wealthy and injecting "ideological issues into what should be a simple debate about cutting taxes for the middle class."