There were two messages from Republicans on the morning after their sweeping victory in the 2014 midterm elections. One was that voters had elected Republicans to stop President Barack Obama’s agenda. The other was that voters had elected Republicans to depose Harry Reid and break the gridlock in Congress. Both messages are correct, and reconciling them will be the toughest task facing new Senate Majority Leader Mitch McConnell.

The first, and decisive, test will be Obama’s proposed executive amnesty, through which–it is suggested–he may try to defer indefinitely the deportations of millions of people who broke the law to enter and/or stay in the United States. Alarmingly, McConnell failed to mention to topic of amnesty in his joint op-ed with Speaker of the House John Boehner in his Thursday morning op-ed in the Wall Street Journal setting their new agenda.

At Wednesday’s postmortem press conference, Obama was not asked whence he might derive the constitutional authority for his proposed executive orders–what the tech sector calls, euphemistically, “administrative relief.” He has no such authority. Yet it is difficult to see how Obama can be stopped, since impeachment is well off the table, and since the House of Representatives’ lawsuit on related matters has turned out to be a bit of a joke.

McConnell, furthermore, has tied his own hands by promising that he will not threaten or use a government shutdown to enforce Congress’s will. Conservatives are seething at that tactical retreat, pointing out the the 2013 shutdown had no effect on the GOP’s electoral fortunes. Yet the more basic problem is that a shutdown is not a credible threat, simply because there are too many GOP Senators up for re-election in blue states in 2016.

The lesson that McConnell took from the shutdown–the proverbial “second kick of a mule”–is that any threat made in political confrontations with the White House must be a credible one.

There are some fights worth losing: for example, Republicans in both houses should repeal Obamacare and pass the Keystone XL pipeline, knowing that Obama will certainly veto the legislation, if only to show the public what the stakes are in 2016.

Otherwise, McConnell’s tools are very limited. He will have a small majority of votes within his own party, and Democrats, sensing potential gains in 2016, are unlikely to cross over to help. Between Ted Cruz on the one hand and John McCain on the other, McConnell also has a fractious caucus that will be difficult to unite in a confrontation.

He has only one real power that no one else can take away: the power to bring bills to the floor.

That means McConnell can block any and all of Obama’s appointments, both executive and judicial. And that is what McConnell should threaten to do if Obama attempts to carry out executive amnesty. It is a threat that is directly related to the powers that Obama proposes to abuse, and it is better than threatening to defund the government or even particular agencies, which would have the disadvantage of punishing innocent individuals.

If Obama persists, then defunding is on the table–but it should remain targeted. And it should aim directly at the White House itself, cutting funding for all positions necessary to carrying out the president’s non-security powers, even grounding Air Force One if necessary.

McConnell should be prepared, ultimately, to defund the White House–even while passing the rest of the legislation that he and Boehner have on their long to-do list.

Senior Editor-at-Large Joel B. Pollak edits Breitbart California and is the author of the new ebook, Wacko Birds: The Fall (and Rise) of the Tea Party, available for Amazon Kindle.

Follow Joel on Twitter: @joelpollak