The new Republican House is likely to run into a brick wall in the Senate on most issues. Sure, they’ll try to repeal the health care law, but would need 13 Democrats in the Senate to join them on that. They have Darrell Issa and his subpoena power, and he’s likely to be quite effective, but that’s not legislation so much as a sideshow tent.

But where Republicans will try to make headway is through the appropriations process. On health care, Mitch McConnell basically laid out the prospects of de-funding the health care law if they can’t get their way on repeal. Congress would have to affirmatively pass appropriations, so a roadblock or veto pen doesn’t work in this context.

If Obama should veto laws repealing the health care overhaul, Senate Minority Leader Mitch McConnell says, the House should cancel funding for its programs. As for the Senate, he says that senators should vote against what he calls the law’s “most egregious provisions.”

In remarks prepared for a speech Thursday to the conservative Heritage Foundation, McConnell says it’s all part of the effort to deny Obama a second term in the White House in 2012.

I don’t see a way forward on that, but in McConnell’s remarks on raising the debt limit, a failure to do which could set off a global financial panic, you can see how he’ll try: through brute intimidation and threats.

In an interview with Fox News this evening, Senate Minority Leader Mitch McConnell said Congress would not vote to increase the nation’s debt ceiling — legislation that must pass to avoid a global economic panic — without “strings.” Those strings could be attached to anything, including health care legislation.

John Boehner, when asked about this at yesterday’s Republican press conference, said he would be “working that out over the next couple of months.”

There’s some thought to getting the debt limit increased in the lame duck session, but I doubt they would be able to pass something on the order of $2 trillion dollars, enough to provide a cushion through the entire 112th Congress. That’s not typically how it works. Anyway, they’d need the support of two Republicans in the Senate (Mark Kirk will replace Roland Burris for the lame duck), along with Ben Nelson and Joe Manchin (who replaces Carte Goodwin). I think it’s a numbers problem as much as anything, along with the fact that Mitch McConnell will put the screws to anyone in his caucus who even thinks about taking away this bargaining chip.

This is very dangerous. Failure to raise the debt limit may be something the Treasury Department can paper over for a little while, but aside from some essential government functions shutting down, it runs the risk of eventual default or just a loss in confidence from investors. The effects could be catastrophic. That’s the kind of grenade McConnell and the Republicans like to have in their hands. They’re going to want something in return for not blowing up the entire global economy. Nobody yet knows what that will be.

UPDATE: To be sure, Obama has some leverage in this as well. He could threaten to veto anything, including cherished tax cuts, that doesn’t pay for itself, and have a pretty good argument to make to the public (even though the economy needs some unpaid-for spending right now). I could see a debt limit-for-tax cut extension possibility, which would be stupid but probably the least harmful world at this point.

UPDATE II: This is what leadership means to McConnell:

“While clearly the election did not transfer full control of the government to the opposition, it is the first step in changing the direction of what we have been doing in Washington,” McConnell said. Republicans will “work with the administration when they agree with the people and confront them when they don’t,” McConnell warned.

And who decides when the Administration agrees with the people? Mitch McConnell. Furthermore, this is what they said when they were in the deep minority, too.

UPDATE III: President DeMint on this:

King: A question first on what comes ahead. Many have said that now that the Republicans have the house and more conservatives in the Senate, when will we know if you’re serious about keeping your promises about spending and the debt. If there is a vote in the congress on raising the debt ceiling, so that the government can continue to print money and spend money should the Republicans say no?

DeMint: I think Republicans will say no. Unless the raising of the debt ceiling is accompanies by some dramatic spending cuts, something that will direct us to a balanced budget in the future, Republicans will not support an increase in the debt limit.