Can congressional Republicans repeal Obamacare? House Speaker John Boehner spoke with the media soon after the Supreme Court's ruling last Thursday. Republicans say they can use reconciliation to overturn large parts of Obamacare Reconciliation lets a bare Senate majority change certain tax and spending rules GOP leaders are also using the issue to fire up their conservative base Chief Justice Roberts called the mandate a tax in last Thursday's ruling Washington (CNN) -- While conservatives are still seething over last week's Supreme Court ruling saving President Barack Obama's health care overhaul, top Capitol Hill Republicans are gleefully using the decision to fire up their base with promises of a repeal in 2013. The high court's 5-4 decision "underscores the urgency of repealing this harmful law in its entirety," House Speaker John Boehner, R-Ohio, said shortly after last Thursday's ruling. Republicans stand ready to work with a president who will listen to the American people. House Majority Leader Eric Cantor, R-Virginia, announced that his GOP-controlled chamber will vote on a full repeal on July 11. While the House is certain pass the measure -- it's already done so once before -- the largely symbolic bill has no chance of clearing the Democratic-run Senate. But what if Mitt Romney is elected president in November while Republicans hold the House and win a majority in the Senate? Could that be enough to undo Obama's signature legislative accomplishment? Top GOP strategists believe they could essentially gut the law, thanks in part to the wording of Chief Justice John Roberts' controlling opinion. Read the high court's Obamacare ruling Roberts ruled that the controversial individual mandate -- the core part of the law forcing Americans to pay a fine if they don't have health insurance -- is actually a tax. And a complex congressional rule known as reconciliation would allow Republicans to change certain tax and spending components of the health care law with only a bare Senate majority. "The chief justice said (the mandate) is a tax, and taxes are clearly what we call reconcilable," Senate Minority Leader Mitch McConnell, R-Kentucky, said on Fox News Sunday. That's the kind of measure that can be pursued with 51 votes in the Senate. And if I'm the leader of the majority next year, I commit to the American people that the repeal of 'Obamacare' will be job one. The reconciliation process could also be used to strip funding for the statute, one senior GOP strategist told CNN. Reconciliation matters because in today's sharply polarized political climate, most legislation can't clear the 100-member Senate without a filibuster-proof of majority of 60 votes. Right now, the Republicans control 47 Senate seats. While most political analysts believe the GOP has a decent shot at a net pickup of four seats this fall, almost nobody believes the Republicans can gain 13 seats. In the meantime, top congressional Republicans have latched onto the notion that the individual mandate is a tax -- something GOP leaders believe plays into one of the Democrats' main political weaknesses. Obamacare is "not a good idea (and) I think you saw one of the reasons why -- because it's a tax increase," Florida Sen. Marco Rubio, a possible GOP vice presidential nominee, said Saturday. It's a massive tax increase on the middle class. While Democratic leaders still maintain the mandate is not a tax -- instead calling it a penalty -- roughly 60% of Americans believe it is, according to a CNN/ORC International poll released Monday. The poll also notes that while an overwhelming majority of GOP voters oppose the mandate, 55% of independents do as well. Republican Senate candidates are now being told that "every day you are not talking about (the health care issue) is a day you've wasted," according to a Washington-based GOP strategist. One potential wrinkle in any GOP plans to call the individual mandate a new Democratic tax: Romney's health care overhaul in Massachusetts also included a mandate. "This was a plan that, that Gov. Romney supported," White House Chief of Staff Jack Lew said Sunday on CNN's "State of the Union." It's something that I would think that he would have been proud of. Pressed on the issue Monday, Romney senior campaign adviser Eric Fehrnstrom told MSNBC that the presumptive GOP presidential nominee agrees "with the dissent written by Justice (Antonin) Scalia which very clearly stated that the mandate was not a tax." Fehrnstrom bucks Republican line on 'Obamacare' as 'tax' Asked repeatedly if Romney agrees with Obama and Democrats that the penalty tied to the mandate is not tax, Fehrnstrom eventually said, "That's correct."