House Speaker John Boehner told Republicans in a closed-door meeting Tuesday that the House doesn't need to pass a third ...

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House Speaker John Boehner told Republicans in a closed-door meeting Tuesday that the House doesn't need to pass a third sequester replacement bill before the "Senate gets off their ass and passes it once."

It's a familiar refrain from the Ohio Republican, who has consistently criticized the Senate for failing to act to blunt the sequester. The call for the Senate to move legislation came at a meeting at the Capitol Hill club.

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"It's time for the Senate to act," Boehner said during a media availability after the meeting. "It's not about the House. We've acted. Where's the president's plan to avoid the sequester? Have you seen one? I haven't seen one. All I've heard is he wants to raise taxes again. Where's the president's plan? Where's the Senate Democrats' plan? I want to see it."

President Barack Obama plans to travel to Newport News, Va., on Tuesday to highlight the effect of the sequester on the military. He will be accompanied by several lawmakers, including Virgina GOP Rep. Scott Rigell.

(WATCH: Boehner: Obama using military as prop)

House Republicans passed their plan to replace sequester cuts with cuts of their own in the 112th Congress, rendering it useless during this session. Boehner said his chamber will "be prepared to move quickly" if the Senate passes a bill.

Action in the upper chamber is coming. The Senate will vote on dueling plans this week designed to stave off the $85 billion, across-the-board spending cuts known that are set to take effect on Friday.

Senate Democrats plan to take up a bill that will replace the sequester with a mix of spending cuts and revenue, mostly garnered from a minimum 30 percent tax on millionaires known as the "Buffett Rule." That approach, however, is a nonstarter with Republicans because of its focus on tax hikes.

Senate Republicans are currently trying to decide whether to offer their own alternative to the Democratic bill, which would give Obama more flexibility in implementing the automatic spending cuts. Both bills would likely need to surmount a 60-vote threshold when the votes are held on Wednesday or Thursday -- and both are likely to fail.

(Also on POLITICO: Sequestration: Bring it on!)

But top Senate Republicans worry about placing so much power in the hands of a Democratic president, who would be able to wield the budget-cutting knife at will.

"I spent long hours writing the defense [authorization] bill," McCain told POLITICO, "I'm not about to give up my constitutional obligations to the President of the United States."

"I think the appropriations process belongs in the legislative branch," said Sen. Marco Rubio (R-Fla.). "And to give the administration carte blanche to decide what they're going to fund and not fund, as you're already seeing in some of the statements they're putting out, they're trying to in some ways to maximize the destruction that this creates for political purposes."

House Republicans have said they will not pass any sequester replacement bill that contains tax hikes. Most blame the sequester on Obama.

Barring any action in the Senate and a last-minute deal between the White House and lawmakers, the sequester is likely to go into effect on March 1.

At the beginning of the Senate's session Tuesday, there was little hope for a last-minute deal."The consequence of the so-called sequester cuts are real not only for national defense but for millions of American families and businesses alike," Senate Majority Leader Harry Reid (D-Nev.) said on the floor. "Three-quarters of a million jobs, 750,000 jobs, Mr. President, are at stake."

Reid added that the "only" Republicans who oppose the Senate Democrats' approach "are the Republicans who serve here in Congress."

Senate Minority Leader Mitch McConnell (R-Ky.) fired back, saying Obama was presenting the country with two options: "Armageddon or a tax hike."

"Well, it's a false choice, and he knows it," McConnell said. "But then, the President's a master at creating the impression of chaos as an excuse for government action. Do nothing. Fan the flames of catastrophe. Then claim the only way out is more government, in the form of higher taxes."

The sequestration is giving lawmakers an opportunity to engage in one of their favorite past times: Doling out pithy one liners.

At a press conference on Tuesday morning, Minority Leader Nancy Pelosi (D-Calif.) drew giggles from her own staff and fellow members as she chastised House Republicans for what she called inaction.

They're not kicking the can down the road.

"They're nudging the potato across the table with their noses," she explained.

Manu Raju and Ginger Gibson contributed to this story.