Sen. Ted Cruz, R-Texas, said Friday that the House should send “one continuing resolution after another funding each specific piece of government,” starting with the military, to pressure Democrats to keep the armed forces operational while agencies charged with implementing Obamacare stand without funds.

In other words, Cruz is calling on the House to “show courage” by passing a bill it has already sent to the Senate.

“I think the House can systematically respond. I hope they would respond to the Senate if Harry Reid does try to force a government shutdown by passing one continuing resolution after another funding each specific piece of government, starting off with funding the military. Send it over and say, ‘Alright Harry Reid, are the Senate Democrats, is President Obama, going to shut down the military? Is that what you want to do?” Cruz said on Fox News. “For things like funding the military, I would send it as a clean, focused continuing resolution.”

The problem: On June 4, the House passed an appropriations bill to cover Military Construction-VA. On July 24, the House approved its Defense appropriations bill. The House has passed two additional appropriations bills. So passing another bill would be repetitive.

Cruz earlier Friday called on GOP Senators to filibuster a three-month continuing resolution passed by the House on Friday, because he says Senate Democrats will otherwise strip out language intended to defund Obamacare.

Of course, the road to enactment has been rocky for both the Military Construction-VA and the Defense spending bills. The Senate has not moved to take them up. And President Barack Obama has threatened to veto them because administration officials want a comprehensive approach to dealing with budget issues, especially as Republicans fought to raise defense spending levels after the sequester was enacted in March.

Meanwhile, not every Texas Republican is as excited about the possibility of government shutdown, which would likely ensue if senators heeded Cruz’s advice to filibuster the CR. Sen. John Cornyn, R-Texas, told the Austin American-Statesman that the GOP could not shut down the government over defunding the president’s health care law.

“I know that some people are discussing filibusters, but I actually think we’re at the point now where we can’t shut down the government — it’s like burning down the house to get rid of the mice or rats,” the No. 2 Senate Republican said.

Niels Lesniewski contributed to this report.