John McCain nailed down the Republican presidential nomination on Tuesday night, winning all four state primaries to knock out his main challenger, Mike Huckabee, while Hillary Clinton pulled off three wins to keep the Democratic race tied up. McCain then received the endorsement of US President George W. Bush, who hosted him at the White House Wednesday and praised him, saying, "He understands this is a dangerous world, and I understand we better have steadfast leadership who has got the courage and determination to pursue this enemy, so as to protect America." In his victory speech claiming the nomination on Tuesday night, McCain laid out general election campaign themes making the wars in Iraq and Afghanistan and the overall fight against "violent extremists" central issues. Beginning his recitation of policy priorities, McCain spoke about the need to bring the Iraq war to "the swiftest possible conclusion" without triggering further sectarian conflict or even genocide and without "destabilizing the entire Middle East, enabling our adversaries in the region to extend their influence and undermine our security there, and emboldening terrorists to attack us elsewhere with weapons we dare not allow them to possess." He also pressed the need to enlist greater support from allies in the fight against al-Qaida and to reorganize the US's military, intelligence agencies and diplomatic efforts "to combat Islamic extremism, encourage the vast majority of moderates to win the battle for the soul of Islam, and meet the many other rising challenges in this changing world." McCain delivered a pointed thanks to all the independent and "independent-thinking" Democrats who have helped power him to victory even though many traditional conservative groups continued to support Huckabee. By Tuesday night, McCain had earned more than half of the delegates to September's Republican nominating convention, which officially declares the nominee. Despite much of the public's current dissatisfaction with the Republican Party, McCain is counting on his cross-over appeal to make him a formidable candidate in the fall, a race that he can beginning running while the Democrats are at a standstill. Hillary Clinton's healthy wins in Ohio and Rhode Island and narrow victory in Texas have re-energized her campaign, which was flagging after 11 straight losses to Barack Obama. However, Obama still leads in the number of national nominating convention delegates, picking up almost as many on Tuesday as Clinton did. Obama's camp believes the delegate deficit will be too great for Clinton to overcome, and the candidate tried to portray himself Tuesday as already in a two-way race. "In the coming weeks, we will begin a great debate about the future of this country with a man who has served it bravely and loves it dearly," Obama said of McCain in his speech, noting that he had called his competitor to congratulate him on winning the Republican nomination. But Obama also spoke of their contrasting visions, characterizing McCain's stance as one that "continues to divide and isolate America from the world by substituting bluster and bullying for direct diplomacy - by ignoring our allies and refusing to talk to our enemies, even though presidents from Kennedy to Reagan have done just that; because strong countries and strong leaders aren't afraid to tell hard truths to petty dictators." Yet Clinton also referred to a race between herself and McCain, telling supporters Tuesday night, "I congratulate Sen. McCain on winning his party's nomination, and I look forward to a spirited and substantive debate with him." She also addressed America's international challenges, saying, "We're ready to reach out to our allies and confront our shared challenges. We're ready to end the war in Iraq and win the war in Afghanistan." There had been widespread speculation about whether Clinton would drop out of the race if she fared poorly on Tuesday night. But her wins in Texas, Ohio and Rhode Island gave her enough momentum to carry on. She proved victorious largely by reestablishing her support with her base constituencies, many of whom had tilted toward Obama in the most recent primaries - blue-collar, female and Latino voters. Exit polls did not sample enough Jewish voters to make it clear Wednesday whether Clinton had also regained widespread backing from Jews, who had favored her by large margins early on, but who had split their votes between the two candidates in recent weeks. A sizable Jewish population will head to the polls on April 22 in Pennsylvania, the next - and last - large state to vote in the primaries. Wyoming caucuses and Mississippi primaries will come first, but their delegates are well out-numbered by Pennsylvania's. After that, eight smaller state contests remain. Super delegate votes, however, are also up for grabs, and the candidates have been wooing these party heavyweight and elected officials, who could prove crucial in determining who gets the nomination.