President Donald Trump's Supreme Court nominee Brett Kavanaugh visited top U.S. Senate Republicans on Capitol Hill on Tuesday, seeking to build support among lawmakers in what promises to be a contentious confirmation battle with Democrats. Top Senate Democrat Chuck Schumer vowed an all-out battle against Kavanaugh, but senators in his party cannot block Kavanaugh's confirmation if no Republicans break ranks. Trump's fellow Republicans hold a 51-49 Senate majority, leaving them little margin for error. Advocacy groups for and against Kavanaugh planned to spend millions of dollars in advertising to try to sway lawmakers. The morning after being nominated by Trump for a lifetime seat on the nine-member conservative-majority court, Kavanaugh began making the rounds in the Senate, first visiting Republican leader Mitch McConnell and then Judiciary Committee Chairman Chuck Grassley, whose panel will hold confirmation hearings. Vice President Mike Pence, who holds a tie-breaking vote in the Senate, accompanied Kavanaugh to the meeting with McConnell. "We look forward to the confirmation process, which will unfold in the next few weeks," McConnell said, ignoring a question about whether Democrats would support the nomination. Kavanaugh, a conservative appeals court judge, did not respond to questions. McConnell told reporters later in the day he hoped for a confirmation vote "sometime this fall." Other Republicans said they hoped to confirm Kavanaugh before the court reconvenes in October. Republicans want a speedy process to ensure the vote is held well before the Nov. 6 midterm elections in which all 435 seats in the House of Representatives and 35 of the 100 Senate seats are up for grabs, with Democrats trying to seize control of Congress. "I will oppose this nominee with everything that I've got," Schumer told MSNBC, warning that a more conservative court including Kavanaugh could overturn the landmark 1973 Roe v. Wade ruling legalizing abortion and end protections under the Affordable Care Act healthcare law known as Obamacare. Advocacy groups are targeting five senators as pivotal in the confirmation fight. Democrats plan to pressure two moderate Senate Republicans, Lisa Murkowski of Alaska and Susan Collins of Maine, to oppose the nomination. Both senators have been non-committal toward Kavanaugh's nomination. 'JUDICIAL TEMPERAMENT' "He clearly is qualified for the job, but there are other issues involving judicial temperament and his judicial philosophy that also will play into my decision," Collins told reporters. Republicans will target three Democrats facing re-election in conservative states where Trump won big majorities in the 2016 election - Heidi Heitkamp of North Dakota, Joe Manchin of West Virginia and Joe Donnelly of Indiana - to support Kavanaugh. All three Democrats have touted their ability to work with Trump. They all voted last year to support Trump's first Supreme Court nominee, Neil Gorsuch, but have been non-committal on Kavanaugh. Kavanaugh is Trump's second nominee, giving the president a chance to solidify conservative control of the court for years to come. The Judicial Crisis Network, which pushes for conservative judicial nominees, will launch a $1.4 million ad campaign aimed at Donnelly, Heitkamp and Manchin, according to a representative for the group. Americans for Prosperity, a conservative policy advocacy group backed by the influential Koch network, has planned a seven-figure ad campaign to support Kavanaugh, as it did last year on behalf of Gorsuch, as well as mounting a grassroots campaign in Indiana, North Dakota and West Virginia. A new liberal interest group, Demand Justice, plans to spend as much as $5 million to push Democrats to oppose Kavanaugh, and try to persuade Republicans Collins and Murkowski to do the same. Kavanaugh, 53, was nominated to replace retiring conservative Justice Anthony Kennedy, 81. Kavanaugh has served for 12 years on the influential U.S. Court of Appeals for the District of Columbia Circuit, giving him an extensive judicial record that is likely to be revisited at Senate hearings. "Now the tough job for all of us is to go to work. We've got some due diligence," Murkowski told reporters.