Updated: May 11, 3:50 p.m.

The White House is wasting no time getting its campaign under way to sell Supreme Court nominee Elena Kagan to the Senate, with an onslaught of phone calls and Hill visits on tap this week in preparation for a final vote by the July Fourth recess.

President Barack Obama on Monday announced Solicitor General Kagan as his choice to replace retiring Justice John Paul Stevens. The president called on the Senate to “act in a bipartisan fashion” and to “do so as swiftly as possible,” just as it did in confirming Kagan to be solicitor general last year.

The race to confirm Kagan in time for the Supreme Court’s fall term is on: Kagan is already making courtesy calls to Senators in the lead-up to her confirmation hearings. White House officials said Kagan won’t wrap up her phone calls this week since, if she follows in the footsteps of Justice Sonia Sotomayor, she has 88 calls ahead of her.

“We’ll start this week, and they’ll go on for several weeks,” said Ron Klain, chief of staff to Vice President Joseph Biden.

In the meantime, Obama on Monday reached out to Senate Majority Leader Harry Reid (D-Nev.), Minority Leader Mitch McConnell (R-Ky.) and Judiciary Chairman Patrick Leahy (D-Vt.) to talk about his selection of the former Harvard Law School dean. He also called but was unable to reach Judiciary ranking member Jeff Sessions (R-Ala.).

Senior White House officials also have begun stepping up their roles to move the process along. White House Chief of Staff Rahm Emanuel on Monday called at least two Senate Republicans — Maine Sens. Olympia Snowe and Susan Collins — who voted to confirm Kagan as solicitor general in March 2009. And White House Deputy Counsel Susan Davies is being dispatched to the Hill to meet with Senators as the process unfolds. Davies, who formerly worked under Leahy, was also involved in shepherding Sotomayor’s nomination through the chamber.

[IMGCAP(1)]The Obama administration was hoping to corral support early and prevent immediate naysayers. But Republicans didn’t waste time criticizing her credentials, and at least one conservative Senator is already vowing to vote “no.” Sen. James Inhofe (R-Okla.) said Monday that he has concerns about the high court nominee’s “seeming contempt” for the confirmation process, a reference to her description of it in 1995 as “a vapid and hollow charade.” He also criticized “her lack of impartiality” when dealing with people who disagree with her positions.

“The position for which she has been nominated has lifetime tenure, and it is concerning that the president has placed such trust in a nominee that has not been properly vetted through a judicial career, having worked mostly in academia and never before as a judge,” the Oklahoma Republican said in a statement.

But Leahy, who is scheduled to meet with Kagan this week, dismissed the idea that there would be much GOP opposition to the selection. He predicted a smooth and timely confirmation process and said the Senate would vote on her nomination later this summer. Some Democratic aides speculated that Kagan could be confirmed as soon as the July Fourth recess.

“Obviously, we will finish it this summer so she can be sitting on the court when they go back into session in September or October,” Leahy told reporters.

The Judiciary chairman predicted that hearings would follow a similar timeline to that of Justice Sonia Sotomayor: She was nominated to the high court on May 26 last year, sat for her first confirmation hearing July 13 and was confirmed on Aug. 6.

White House Press Secretary Robert Gibbs echoed similar sentiments Monday, saying that the administration is “much farther ahead of the calendar than we were last year” and, because of that, “we would certainly expect that this nomination, that a hearing can happen and a vote can happen before the Senate goes home in August.”

Gibbs said to expect Kagan, if confirmed, to recuse herself from about a dozen cases next year and “maybe less than half of that in the year after, due to conflicts of interest from her role as solicitor general. Kagan argued the controversial campaign finance case Citizens United v. Federal Election Commission on behalf of the United States.

Those estimates are based on analyses from “commentators very familiar with the potential caseload that the next Supreme Court term is likely to include,” Gibbs said.