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Senate Republican Leader Mitch McConnell, in an attempt to pluck an arrow out of President Obama's rhetorical quiver, tried to get the Senate to vote on the president's $447 billion jobs bill Tuesday -- presumably to test whether Democrats have the votes to pass it.

But while Obama repeatedly has called on Congress to pass the bill right away, Democratic Leader Harry Reid shot down the effort, accusing McConnell of pulling a political stunt.

"I am disappointed that he would play games with this important legislation," Reid said, pledging to take up the bill later on in the session.

The back-and-forth marked the latest bout of brinkmanship as Congress weighs how to approach a bill which, while labeled a priority by the president, may not have the bipartisan support needed to pass in one piece.

The president stopped in Texas on Tuesday to once again urge Congress to pass the American Jobs Act.

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"It's time to pass this jobs bill and get America working again," Obama said, griping that it's been three weeks since he sent it to Congress.

McConnell, on the Senate floor shortly before the speech, said Obama "is entitled to a vote." He offered it as an amendment to a separate bill dealing with China currency.

After Reid objected, McConnell spokesman Don Stewart blasted out a memo to the press suggesting complaints from within Reid's own caucus could be behind his reluctance to move forward.

Sen. Lamar Alexander chimed in with some more ribbing.

"Senator McConnell is trying to give the president the vote he requested. How can the Democratic leader now in good conscience object to the vote the president has been asking for?" Alexander, R-Tenn., said in a statement.

While McConnell tried to fast-track the package to the floor Tuesday, Republicans are by no means in favor of it.

House Republican Leader Eric Cantor said Monday the bill is dead on the House side.

Cantor told reporters the GOP is ready to "work together" on parts of the president's proposal, but Republicans won't stand for taking up the bill as a take-it-or-leave-it deal.

"Now, the president continues to say, pass my bill in its entirety. As I have said from the outset, the all-or-nothing approach is just unacceptable," Cantor said.

The GOP leader said the House would carve out and act on a proposal to end a requirement that the government withhold 3 percent of payments to contractors. He also said the House would act on the three free-trade agreements the White House sent to Congress for Colombia, Panama and South Korea -- a long-delayed set of measures the president has highlighted in prior jobs speeches, though he did not send them to Congress until this week.

The White House says the overall legislation will keep 280,000 teachers in the classroom, add tens of thousands more and pay for modernization of at least 35,000 public schools buildings.

On Monday, Obama urged Congress to pass the bill by the end of the month. The president, speaking at Eastfield College in Mesquite, Texas, on Tuesday, singled out Cantor for resisting a vote in his chamber.

"What's the problem? Do they not have the time? They just had a week off," he said, again urging a vote in Congress "so that the entire country knows exactly where members of Congress stand." He did not mention McConnell.