Story highlights Ted Cruz rallied House conservatives against a proposed plan to avoid a government shutdown

Cruz was seen as largely responsible for the government shutting down last year

Cruz has repeatedly rejected that claim, and said it's Democrats who risk causing a shutdown

When Sen. Ted Cruz, R-Texas got out of his car at the Capitol on Wednesday, he did not to go into the Senate where he works. He was on the House side to join a conservative rally to press their own GOP leaders to use the power of the purse to fight the president on immigration.

Since the day Cruz was sworn in almost two years ago, he has proudly been a thorn in House Republican leaders' side -- urging them to put principle before practical politics.

Last year the government shut down thanks to a strategy pushed by Cruz to tie defunding Obamacare to funding the government.

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But even then he didn't take the extra step, literally, to physically go to the House and, symbolically, put his thumb in the eye of House Speaker John Boehner. Today, he did.

On his way to the podium, this reporter asked why he is inserting himself in what the House is doing.

"I don't agree with the premise of what you're saying," Cruz responded.

"Republicans campaigned saying if you elect us, if you elect a Republican Senate, we will stop President Obama's illegal acts. These elections were a referendum. The American people overwhelmingly said they do not support a lawless amnesty created by the President. What I'm urging Republicans to do is -- do what we said we would do -- honor the commitments of the American voters," Cruz continued.

Cruz wants House Republicans to attach a policy rider to the bill funding the government that denies the President his executive action allowing some 5 million undocumented workers legal status.

But since the government runs out of money on Dec. 11, leaders in both chambers don't want to have that fight right now. Instead they want to pass a bill funding most of the government for a year, and only fund the Department of Homeland Security, which oversees immigration laws, for a few months. They're hoping that will buy them time to find an option to fight the President, even while conceding there are no good options.

Frustrated House GOP leadership aides argue that Cruz pushing to have a fight now is disingenuous because it is unwinnable. The Senate is still run by Democrats and they will not pass a bill effectively canceling out the president's executive authority, never mind that the president would never sign such a bill even if he got it.

When asked about this GOP criticism, and concern that his strategy could once again lead to a government shutdown, Cruz balked.

"No it's not. And it only will if Harry Reid decides he wants a shutdown, which it seems Harry Reid and President Obama are very eager about that prospect."