The saying, "Be careful what you wish for, it might just come true" was especially relevant on Capitol Hill Wednesday.

Speaker John Boehner (R-Ohio) announced the House will advance a measure to keep the government running and defund Obamacare -- just like Sens. Mike Lee (R-Utah), Ted Cruz (R-Tex.) and their conservative allies have been demanding.

Sen. Mike Lee (R-Utah) and Sen. Ted Cruz (R-Tex.) (AP Photo/J. Scott Applewhite)

Cruz, one of the most vocal Obamacare opponents in Washington, cheered the news, telling National Review's Robert Costa he "salutes" Boehner. Lee, meanwhile, called it a "victory for the American people."

But they may have bitten off more than he can chew.

Here's the reality of what just went down: House GOP leaders have set up a situation that allows them to hand the effort to defund Obamacare off to the Senate, where it stands no chance of succeeding. Lee, Cruz and a handful of other Republican senators have gained hardly any traction in their push to shred Obamacare, and that's not about to change.

There has been little appetite among other Senate Republicans to defund Obamacare in a continuing resolution because President Obama would never sign it and the resulting standoff could trigger a government shutdown. Many Republicans don't want to be blamed for a shutdown. After lobbying publicly for weeks, Lee, Cruz and others have only been able to cobble together a coalition of about a dozen senators on the issue.

That tough reality is about to be amplified. The conservative senators are not likely to change many more minds once a bill comes to the Senate. So when the push to defund Obamacare inevitably goes down, they -- not House GOP leaders -- will be the ones held responsible.

Here's the most likely scenario in the Senate: Majority Leader Harry Reid (D-Nev.) will strip the provisions to defund Obamacare from the CR, set a vote in which it will pass, and send it back over to the House. (Boehner will once again have a problem on his hands, but that's another story.) House GOP leaders can say it used the CR fight to try to defund Obamacare, but Senate conservatives weren't able to do the heavy lifting in their chamber.

What's more, from a procedural standpoint, the defund hard-liners in the Senate may find themselves presented with the dilemma of whether to try to filibuster the bill they asked for. The stripping of the defunding language wouldn't come until after all cloture votes have passed and only a simple majority would be required for final passage. In other words, the only way Cruz could stop Reid from passing the bill would be to filibuster.

It's hardly an enviable position to be in.

"Harry Reid will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so," Cruz said in a statement. "At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people."

Of course, even if Cruz is blamed for failing to defund Obamacare, he's not likely to suffer much damage to his image in the eyes of his most loyal supporters. If anything, they'll laud him and his allies for taking up the fight in the first place.

But the limits of their power would be exposed, they would no longer be able blame House Republican leaders for failing to act, and the issue on which they have fought tooth and nail would have just suffered a tangible setback on their watch.

And if a government shutdown happens, Cruz and his cohorts could also stand to absorb a lion's share of the blame for that. He was a vocal part of House and Senate movement to defund Obamacare that painted Boehner into a corner. If time runs out on lawmakers to strike a deal, we could hear a whole lot of "I-told-you-so" comments lobbed at Cruz and his allies from his own party.

And that could diminish their power and influence in Congress the next time a big debate erupts.

Updated at 5:17 p.m.