Senate majority leader Harry Reid gestures as he speaks to the media as lawmakers moved toward resolving their feud over filibusters of White House appointees on Capitol Hill in Washington, Tuesday, July 16, 2013. Sen. Chuck Schumer, D-N.Y., chairman of the Senate Rules Committee, speaks with reporters just off the Senate floor as lawmakers moved toward resolving their feud over Republican filibusters of White House appointees, at the Capitol in Washington, Tuesday, July 16, 2013. The Senate just voted 71-29 to end a two-year Republican blockade that was preventing Richard Cordray from winning confirmation as director of the Consumer Financial Protection Bureau. WASHINGTON (AP) - A bipartisan Senate pact has smoothed the confirmation path for a batch of President Barack Obama's nominations and removed, for now, a Democratic threat to impose procedural changes weakening minority Republicans' clout. Yet there are no guarantees that the conflict won't flare anew the next time a White House appointment stirs controversy. A day after both parties celebrated an agreement averting a bitter fight over Senate rules, the chamber planned to vote Wednesday on one of Obama's picks, Fred Hochberg to be president of the Export-Import Bank. Also possible this week are roll calls on Labor Secretary-designate Tom Perez and Gina McCarthy, Obama's choice to lead the Environmental Protection Agency. On Tuesday, Republicans agreed to allow quick votes on seven Obama selections by simple majority margins, rather than forcing Democrats to garner 60 votes to succeed. Hours later, the Senate by 66-34 approved the first of those appointments, confirming Richard Cordray to head the Consumer Financial Protection Bureau - after Republicans had blocked him for nearly two years as they demanded changes in the agency's structure and financing. In a written statement, Obama thanked Senate leaders for working out their dispute but criticized his opponents for using "purely political reasons" to stall the nominations. "In the weeks ahead, I hope the Congress will build on this spirit of cooperation to advance other urgent middle-class priorities" like revamping immigration laws and keeping student loan interest rates from rising, Obama said. In exchange for the GOP concessions on the nominations, Democrats agreed to drop their effort to change the chamber's rules. Obama also submitted two new nominees for a pair of labor posts after Republicans adamantly opposed his initial picks. Does that mean it will last forever? I don't know about that," Senate Majority Leader Harry Reid, D-Nev., said of the accord. But he added, "We have a new start for this body, and I feel very comfortable with it." Democrats had been threatening to muscle through a rules change preventing opponents from forcing top agency nominees to win 60 votes from the 100-member Senate. That would have diminished the chamber's filibuster rule that minority parties, Republicans as well as Democrats, have long cherished as a tool that prevents them from becoming virtually irrelevant. Changing the Senate's rules by majority vote - instead of the two-thirds margin usually required when the plan is controversial - is unusual and considered likely to invite such harsh retaliation that it is called the nuclear option. "I think it's a step in the right direction that the majority has chosen not to exercise the nuclear option," Senate Minority Leader Mitch McConnell, R-Ky. We feel good about that. I think they feel good about it. So I think that crisis has been averted. The standoff was resolved following an exceptional closed-door meeting in the Capitol's old Senate chamber Monday night, attended by nearly every senator. For the previous several days, senators had met and made phone calls in an effort to head off a clash, with several lawmakers crediting Sens. John McCain, R-Ariz., and Chuck Schumer, D-N.Y., for helping bring the sides together. As part of the resulting agreement, Obama withdrew his nominations of two nominees to the National Labor Relations Board, Richard Griffin and Sharon Clark. Obama installed Griffin and Clark onto the board in 2011, bypassing the Senate but triggering a legal challenge in which an appeals court has said the two appointments were invalid. Republicans were insistent that those selections be replaced. In their places, Obama nominated Nancy Schiffer, a former top lawyer for the AFL-CIO, and Kent Hirozawa, counsel to NLRB Chairman Mark Pearce. Reid said he was planning for the Senate to confirm both next week. The seventh Obama appointment involved in the bipartisan deal is Pearce, whose pick is relatively uncontroversial. The NLRB appointments, if confirmed as expected, would prevent the virtual shutdown of the agency because of a lack of confirmed board members to rule on collective bargaining disputes between unions and companies. Associated Press writer David Espo contributed to this report.